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Lotka–Volterra Fishing Problem

This example is based on the Lotka-Volterra fishing problem.

Setup

Use Corleone to define the shooting layers and optimization models.

using Corleone

The other packages provide:

  • Layer initialization: LuxCore and Random
  • ODE integration: OrdinaryDiffEqTsit5
  • Optimization: Optimization, OptimizationMOI, Ipopt, and ComponentArrays
  • Objective and constraint gradients: ForwardDiff
  • Plotting: CairoMakie
using LuxCore
using Random
using OrdinaryDiffEqTsit5
using SymbolicIndexingInterface
using Optimization
using OptimizationMOI
using Ipopt
using ComponentArrays
using ForwardDiff
using CairoMakie
Makie.inline!()
Makie.Automatic()

Lotka–Volterra Dynamics

The first two states are prey and predator populations. The third accumulates their squared deviations from one. The second parameter is fishing intensity; the first and third are fixed interaction rates.

\[\begin{aligned} \dot{x} &= x-xy-0.4vx, & x(0)&=0.5, \\ \dot{y} &= -y+xy-0.2vy, & y(0)&=0.7, \\ J &= \int_0^{12}\bigl((x-1)^2+(y-1)^2\bigr)\,dt, & 0&\le v\le1. \end{aligned}\]

Here v is the fishing control, stored as p[2] in the numerical model.

function lotka_dynamics(du, u, p, t)
    du[1] = u[1] - p[1] * prod(u[1:2]) - 0.4 * p[2] * u[1]
    du[2] = -u[2] + p[3] * prod(u[1:2]) - 0.2 * p[2] * u[2]
    return du[3] = (u[1] - 1.0)^2 + (u[2] - 1.0)^2
end
tspan = (0.0, 12.0)
u0 = [0.5, 0.7, 0.0]
p0 = [1.0, 0.0, 1.0]
prob = ODEProblem(lotka_dynamics, u0, tspan, p0; abstol = 1.0e-9, reltol = 1.0e-9)
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: false
timespan: (0.0, 12.0)
u0: 3-element Vector{Float64}:
 0.5
 0.7
 0.0

Single Shooting Approach

Make fishing intensity tunable between zero and one, and keep the two interaction rates fixed. The 119 switching times define 120 control intervals. The initial state is taken from the ODE problem.

cgrid = collect(0.1:0.1:11.9)
control = Tunable(
    2; kind = Val(:parameter), default = 1.0,
    lowerbound = 0.0, upperbound = 1.0
) => cgrid
physical_parameters = (
    Constant([3, 1]; kind = Val(:parameter)) => nothing,
)
layer = ShootingLayer(
    prob, Tsit5(), control, physical_parameters...;
    controls = [2], quadratures = [3]
)
ShootingLayer{}(nothing, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, typeof(Main.var"##336".lotka_dynamics), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, Base.Pairs{Symbol, Float64, Nothing, @NamedTuple{abstol::Float64, reltol::Float64}}, SciMLBase.StandardODEProblem}(SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, typeof(Main.var"##336".lotka_dynamics), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}(Main.var"##336".lotka_dynamics, LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, SciMLBase.DEFAULT_OBSERVED, nothing, nothing, nothing, nothing), [0.5, 0.7, 0.0], (0.0, 12.0), [1.0, 0.0, 1.0], Base.Pairs(:abstol => 1.0e-9, :reltol => 1.0e-9), SciMLBase.StandardODEProblem()), OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Serial}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, FastBroadcast.Serial()), SciMLBase.EnsembleSerial(), InitialConditions{}(nothing, SciMLStructures.ArrayRepack{Vector{Float64}}([0.5, 0.7, 0.0]), (u₁ = PassThrough{}(:u₁), u₂ = PassThrough{}(:u₂), u₃ = PassThrough{}(:u₃)), ([1], [2], [3])), Parameter{}(nothing, SciMLStructures.ArrayRepack{Vector{Float64}}([1.0, 0.0, 1.0]), (p₁ = PiecewiseConstant{}(:p₁, LookUp{}(nothing, nothing), (p₁ = FixedLayer{}(ParameterCollection{}(Corleone.var"#173#174"{Vector{Float64}}([0.0], Core.Box((-Inf, Inf)), Core.Box(1.0)), 1)), p₃ = FixedLayer{}(ParameterCollection{}(Corleone.var"#173#174"{Vector{Float64}}([0.0], Core.Box((-Inf, Inf)), Core.Box(1.0)), 1)))), p₂ = PiecewiseConstant{}(:p₂, LookUp{}([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 9.0, 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 10.0, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9, 11.0, 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.9], nothing), ParameterCollection{}(Corleone.var"#173#174"{Vector{Float64}}([0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 9.0, 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 10.0, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9, 11.0, 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.9], Core.Box((0.0, 1.0)), Core.Box(1.0)), 120))), ([1, 3], [2])), ControlSymbolCache{}(SymbolicIndexingInterface.SymbolCache{Dict{Symbol, Int64}, Dict{Symbol, Int64}, Nothing, Symbol, Dict{Symbol, Float64}}(Dict(:u₃ => 3, :u₁ => 1, :u₂ => 2), Dict(:p₃ => 3, :p₂ => 2, :p₁ => 1), nothing, :t, Dict(:p₂ => 0.0, :u₃ => 0.0, :p₃ => 1.0, :u₁ => 0.5, :u₂ => 0.7, :p₁ => 1.0)), [:p₂], [:u₃], Dict{Any, Any}(:p₂ => (0.0, 1.0))))

Minimize the terminal accumulated cost. The model initializes parameters and state, then prepares the objective. OptimizationProblem applies the control bounds from the annotation and uses ForwardDiff for gradients.

dynprob = CorleoneDynamicOptProblem(
    layer, :(u₃(12.0))
)
opt = OptimizationProblem(dynprob, AutoForwardDiff(); function_kwargs = (;))
uopt = solve(
    opt,
    Ipopt.Optimizer(),
    tol = 1.0e-6,
    hessian_approximation = "limited-memory",
    max_iter = 300,
    print_level = 3
);
@assert successful_retcode(uopt)

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit https://github.com/coin-or/Ipopt
******************************************************************************

Total number of variables............................:      120
                     variables with only lower bounds:        0
                variables with lower and upper bounds:      120
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0


Number of Iterations....: 135

                                   (scaled)                 (unscaled)
Objective...............:   1.3443410156615019e+00    1.3443410156615019e+00
Dual infeasibility......:   9.3110901751459884e-07    9.3110901751459884e-07
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   1.0397554573784411e-07    1.0397554573784411e-07
Overall NLP error.......:   9.3110901751459884e-07    9.3110901751459884e-07


Number of objective function evaluations             = 677
Number of objective gradient evaluations             = 136
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 0
Total seconds in IPOPT                               = 32.260

EXIT: Optimal Solution Found.

Reconstruct the optimized parameters and plot the trajectory.

_, reconstruct = pack(default_vectorizer(), dynprob.ps)
optimized_parameters = reconstruct(uopt.u)
optsol, _ = layer(nothing, optimized_parameters, opt.p)
trajectoryplot(optsol)

Trajectory plot for The Lotka Volterra Fishing Problem

Multiple Shooting

Lift all three states at interior shooting points. Matching constraints enforce continuity, including the accumulated cost, so its final value covers the whole time horizon. Full-state resets allow independent blocks with EnsembleThreads(). Start Julia with --threads=4 to use four threads.

Start with control intervals of length 0.25. The shooting points at 3.4 and 6.1 lie inside intervals; 9.75 already coincides with a control switch.

shooting_points = [3.4, 6.1, 9.75]
initial_conditions = (
    Tunable(i; kind = Val(:variable), lowerbound = 0.0, upperbound = 2.0) => shooting_points for i in 1:3
)
mslayer = ShootingLayer(
    prob, Tsit5(), first(control) => collect(0.25:0.25:11.75), physical_parameters...,
    initial_conditions...; ensemblealg = EnsembleThreads(),
    controls = [2], quadratures = [3]
)
ShootingLayer{}(nothing, SciMLBase.ODEProblem{Vector{Float64}, Tuple{Float64, Float64}, true, Vector{Float64}, SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, typeof(Main.var"##336".lotka_dynamics), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}, Base.Pairs{Symbol, Float64, Nothing, @NamedTuple{abstol::Float64, reltol::Float64}}, SciMLBase.StandardODEProblem}(SciMLBase.ODEFunction{true, SciMLBase.AutoSpecialize, typeof(Main.var"##336".lotka_dynamics), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing, Nothing, Nothing}(Main.var"##336".lotka_dynamics, LinearAlgebra.UniformScaling{Bool}(true), nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, nothing, SciMLBase.DEFAULT_OBSERVED, nothing, nothing, nothing, nothing), [0.5, 0.7, 0.0], (0.0, 12.0), [1.0, 0.0, 1.0], Base.Pairs(:abstol => 1.0e-9, :reltol => 1.0e-9), SciMLBase.StandardODEProblem()), OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Serial}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, FastBroadcast.Serial()), SciMLBase.EnsembleThreads(), InitialConditions{}(nothing, SciMLStructures.ArrayRepack{Vector{Float64}}([0.5, 0.7, 0.0]), (u₁ = InitialCondition{}(:u₁, LookUp{}(Dict(6.1 => 2, 9.75 => 3, 3.4 => 1), nothing), (u₁ = ParameterCollection{}(Corleone.var"#118#119"{Tuple{Float64, Float64}, Float64}((0.0, 2.0), 0.5, Core.Box([3.4, 6.1, 9.75])), 3), u₂ = ParameterCollection{}(Corleone.var"#118#119"{Tuple{Float64, Float64}, Float64}((0.0, 2.0), 0.7, Core.Box([3.4, 6.1, 9.75])), 3), u₃ = ParameterCollection{}(Corleone.var"#118#119"{Tuple{Float64, Float64}, Float64}((0.0, 2.0), 0.0, Core.Box([3.4, 6.1, 9.75])), 3))),), ([1, 2, 3],)), Parameter{}(nothing, SciMLStructures.ArrayRepack{Vector{Float64}}([1.0, 0.0, 1.0]), (p₁ = PiecewiseConstant{}(:p₁, LookUp{}(nothing, nothing), (p₁ = FixedLayer{}(ParameterCollection{}(Corleone.var"#173#174"{Vector{Float64}}([0.0], Core.Box((-Inf, Inf)), Core.Box(1.0)), 1)), p₃ = FixedLayer{}(ParameterCollection{}(Corleone.var"#173#174"{Vector{Float64}}([0.0], Core.Box((-Inf, Inf)), Core.Box(1.0)), 1)))), p₂ = PiecewiseConstant{}(:p₂, LookUp{}([0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 7.75, 8.0, 8.25, 8.5, 8.75, 9.0, 9.25, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75, 11.0, 11.25, 11.5, 11.75], nothing), ParameterCollection{}(Corleone.var"#173#174"{Vector{Float64}}([0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 7.75, 8.0, 8.25, 8.5, 8.75, 9.0, 9.25, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75, 11.0, 11.25, 11.5, 11.75], Core.Box((0.0, 1.0)), Core.Box(1.0)), 48))), ([1, 3], [2])), ControlSymbolCache{}(SymbolicIndexingInterface.SymbolCache{Dict{Symbol, Int64}, Dict{Symbol, Int64}, Nothing, Symbol, Dict{Symbol, Float64}}(Dict(:u₃ => 3, :u₁ => 1, :u₂ => 2), Dict(:p₃ => 3, :p₂ => 2, :p₁ => 1), nothing, :t, Dict(:p₂ => 0.0, :u₃ => 0.0, :p₃ => 1.0, :u₁ => 0.5, :u₂ => 0.7, :p₁ => 1.0)), [:p₂], [:u₃], Dict{Any, Any}(:u₃ => (0.0, 2.0), :u₁ => (0.0, 2.0), :p₂ => (0.0, 1.0), :u₂ => (0.0, 2.0))))

Initialize controls to one and lifted states to the corresponding ODE initial values.

msps, msst = LuxCore.setup(MersenneTwister(42), mslayer)
((initialcondition = (initialconditions = (u₁ = (lookup = NamedTuple(), parameter = (u₁ = (ps = [0.5, 0.5, 0.5],), u₂ = (ps = [0.7, 0.7, 0.7],), u₃ = (ps = [0.0, 0.0, 0.0],))),),), parameter = (parameters = (p₁ = (lookup = NamedTuple(), parameter = (p₁ = NamedTuple(), p₃ = NamedTuple())), p₂ = (lookup = NamedTuple(), parameter = (ps = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],))),)), (initialcondition = (initialconditions = (u₁ = (lookup = (collection = Dict(6.1 => 2, 9.75 => 3, 3.4 => 1), inserted = Int64[], cache = nothing), parameter = (u₁ = NamedTuple(), u₂ = NamedTuple(), u₃ = NamedTuple()), active = false),), active = Bool[0, 0, 0], permutation = [1, 2, 3]), parameter = (parameters = (p₁ = (lookup = (collection = nothing, inserted = Int64[], cache = nothing), parameter = (p₁ = (states = NamedTuple(), parameters = (ps = [1.0],)), p₃ = (states = NamedTuple(), parameters = (ps = [1.0],)))), p₂ = (lookup = (collection = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 7.75, 8.0, 8.25, 8.5, 8.75, 9.0, 9.25, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75, 11.0, 11.25, 11.5, 11.75], inserted = Int64[], cache = nothing), parameter = NamedTuple())), permutation = [1, 3, 2]), timestops = [0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.4, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0, 6.1, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 7.75, 8.0, 8.25, 8.5, 8.75, 9.0, 9.25, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75, 11.0, 11.25, 11.5, 11.75, 12.0]))

Split the control intervals at 3.4 and 6.1, duplicating their current values.

msps, msst = add_parameter_segments!(mslayer, msps, msst)
((initialcondition = (initialconditions = (u₁ = (lookup = NamedTuple(), parameter = (u₁ = (ps = [0.5, 0.5, 0.5],), u₂ = (ps = [0.7, 0.7, 0.7],), u₃ = (ps = [0.0, 0.0, 0.0],))),),), parameter = (parameters = (p₁ = (lookup = NamedTuple(), parameter = (p₁ = NamedTuple(), p₃ = NamedTuple())), p₂ = (lookup = NamedTuple(), parameter = (ps = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0],))),)), (initialcondition = (initialconditions = (u₁ = (lookup = (collection = Dict(6.1 => 2, 9.75 => 3, 3.4 => 1), inserted = Int64[], cache = nothing), parameter = (u₁ = NamedTuple(), u₂ = NamedTuple(), u₃ = NamedTuple()), active = false),), active = Bool[0, 0, 0], permutation = [1, 2, 3]), parameter = (parameters = (p₁ = (lookup = (collection = nothing, inserted = Int64[], cache = nothing), parameter = (p₁ = (states = NamedTuple(), parameters = (ps = [1.0],)), p₃ = (states = NamedTuple(), parameters = (ps = [1.0],)))), p₂ = (lookup = (collection = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.4, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0, 6.1, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 7.75, 8.0, 8.25, 8.5, 8.75, 9.0, 9.25, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75, 11.0, 11.25, 11.5, 11.75], inserted = [15, 27], cache = nothing), parameter = NamedTuple())), permutation = [1, 3, 2]), timestops = [0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.4, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0, 6.1, 6.25, 6.5, 6.75, 7.0, 7.25, 7.5, 7.75, 8.0, 8.25, 8.5, 8.75, 9.0, 9.25, 9.5, 9.75, 10.0, 10.25, 10.5, 10.75, 11.0, 11.25, 11.5, 11.75, 12.0]))

Plot the initial segments and their reset jumps.

mssol, _ = mslayer(nothing, msps, msst);
trajectoryplot(mssol, show_legend = true, whiskerwidth = 10)

Trajectory plot for The Lotka Volterra Fishing Problem

Reuse the expanded parameters and state. State continuity and matching control values at inserted switches are included as equality constraints.

ms_dynprob = CorleoneDynamicOptProblem(
    mslayer, :(u₃(12.0)), ps = msps, st = msst
)

ms_opt = OptimizationProblem(ms_dynprob, AutoForwardDiff(); function_kwargs = (;))
ms_uopt = solve(
    ms_opt,
    Ipopt.Optimizer(),
    tol = 1.0e-6,
    hessian_approximation = "limited-memory",
    max_iter = 1000,
    print_level = 5
);
@assert successful_retcode(ms_uopt)
This is Ipopt version 3.14.19, running with linear solver MUMPS 5.9.0.

Number of nonzeros in equality constraint Jacobian...:      649
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        0

Total number of variables............................:       59
                     variables with only lower bounds:        0
                variables with lower and upper bounds:       59
                     variables with only upper bounds:        0
Total number of equality constraints.................:       11
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  1.3440679e+00 2.41e+00 8.55e-01   0.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  1.2649431e+00 2.39e+00 1.23e+00  -6.2 2.96e+00    -  5.29e-03 8.43e-03h  1
   2  1.1384611e+00 2.36e+00 1.94e+01  -0.5 3.30e+00    -  1.50e-01 1.46e-02h  1
   3  9.8102407e-01 2.31e+00 5.55e+00  -6.3 3.31e+00    -  6.83e-03 1.95e-02h  1
   4  3.4883379e-01 2.32e+00 4.50e+01   0.4 3.49e+01    -  1.69e-02 2.66e-02f  1
   5  1.5180486e-01 2.27e+00 2.11e+02   0.9 2.50e+01    -  5.07e-01 3.05e-02f  1
   6  3.2296180e-01 2.23e+00 2.26e+03   1.9 6.24e+01    -  4.26e-01 1.30e-02f  1
   7  4.7494970e-01 2.15e+00 4.33e+04   2.6 1.54e+01    -  7.98e-01 3.53e-02h  1
   8  5.6293513e-01 1.99e+00 9.04e+04   2.8 2.65e+00    -  1.79e-01 8.35e-02h  1
   9  5.6125931e-01 1.97e+00 1.58e+06   2.8 4.67e+00    -  2.00e-01 1.15e-02h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  5.7183850e-01 1.95e+00 1.24e+08   2.8 2.75e+00    -  7.69e-01 1.04e-02h  1
  11  5.7280755e-01 1.95e+00 3.10e+10   2.8 3.06e+00    -  1.91e-01 7.58e-04h  1
  12  5.7285686e-01 1.95e+00 9.38e+14   2.8 3.77e+00    -  1.00e+00 3.29e-05h  1
  13  1.8950134e+00 2.38e+00 7.25e+14   2.8 2.13e+00    -  2.27e-01 7.06e-01h  1
  14  1.8950049e+00 2.38e+00 1.16e+15   2.8 4.95e+01    -  2.28e-07 5.93e-07f  1
  15  1.8949999e+00 2.38e+00 2.12e+15   2.8 5.96e+00    -  2.26e-09 8.10e-07f  1
  16  1.8252151e+00 2.35e+00 3.03e+15   2.8 1.18e+01    -  4.05e-07 1.38e-02f  1
  17  1.5097128e+00 2.19e+00 2.96e+15   2.8 1.18e+01    -  1.34e-02 6.99e-02h  1
  18  1.5073103e+00 2.19e+00 2.86e+15   1.3 1.18e+01    -  6.87e-02 7.02e-04h  1
  19r 1.5073103e+00 2.19e+00 9.90e+02   1.3 0.00e+00    -  0.00e+00 4.39e-07R  5
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  20r 1.2832252e+00 2.09e+00 7.97e+02   1.8 5.12e+00    -  2.87e-01 1.93e-01f  1
  21r 7.2258771e-01 1.27e+00 1.23e+03   2.3 1.97e+00    -  6.29e-01 4.80e-01f  1
  22  7.1323041e-01 9.98e-01 1.18e+08  -1.1 1.46e-01   9.3 8.77e-01 1.00e+00h  1
  23  6.9768835e-01 9.77e-01 1.17e+08   0.0 5.38e+00    -  8.86e-01 2.14e-02h  1
  24  6.9851690e-01 9.75e-01 1.19e+08   0.7 1.45e+00   8.9 1.00e+00 1.82e-03h  1
  25  6.9855829e-01 9.74e-01 1.19e+08   1.4 5.43e-01   8.4 1.00e+00 9.91e-04h  1
  26  1.2025350e+00 6.00e-01 1.25e+08   2.1 1.61e+00   7.9 1.00e+00 5.05e-01h  1
  27  1.2348279e+00 5.77e-01 1.20e+08   2.2 1.02e+00    -  1.00e+00 3.86e-02h  1
  28  1.9903417e+00 1.57e-01 3.78e+07   2.1 9.85e-01    -  1.00e+00 7.85e-01f  1
  29  2.0109549e+00 1.47e-01 3.57e+07   2.8 2.79e-01    -  4.87e-01 6.68e-02h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  30  1.9697460e+00 8.75e-02 2.15e+04   2.8 3.85e-01    -  9.91e-01 1.00e+00f  1
  31  1.9604427e+00 7.65e-03 3.38e+02   1.6 4.24e-02    -  9.97e-01 1.00e+00f  1
  32  1.9650570e+00 3.19e-05 7.26e+00  -0.3 4.39e-03    -  9.98e-01 1.00e+00f  1
  33  1.9604613e+00 2.88e-05 9.05e-01  -1.4 6.16e-03    -  9.87e-01 1.00e+00f  1
  34  1.8036500e+00 6.37e-03 3.62e-01  -1.5 1.29e-01    -  9.94e-01 1.00e+00f  1
  35  1.5843618e+00 1.84e-02 2.57e-01  -2.1 2.09e-01    -  9.94e-01 1.00e+00f  1
  36  1.4370748e+00 8.10e-03 1.57e-01  -2.4 1.54e-01    -  9.84e-01 1.00e+00h  1
  37  1.3672091e+00 1.15e-02 1.17e-01  -3.1 1.98e-01    -  1.00e+00 1.00e+00h  1
  38  1.3665943e+00 9.11e-04 1.24e-01  -3.1 1.22e-01    -  1.00e+00 9.67e-01h  1
  39  1.3526062e+00 1.65e-03 3.14e-02  -3.6 1.29e-01    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  40  1.3482754e+00 5.77e-04 2.96e-02  -4.1 1.52e-01    -  1.00e+00 7.58e-01h  1
  41  1.3450116e+00 1.67e-03 8.97e-02  -4.6 1.80e-01    -  9.99e-01 1.00e+00h  1
  42  1.3462543e+00 7.15e-04 3.04e-02  -4.2 1.31e-01    -  1.00e+00 1.00e+00h  1
  43  1.3484561e+00 1.20e-05 1.44e-01  -5.0 3.68e-02    -  1.00e+00 1.00e+00H  1
  44  1.3453252e+00 6.95e-04 2.90e-02  -5.5 2.88e-02    -  1.00e+00 7.86e-01h  1
  45  1.3458759e+00 6.38e-05 8.48e-03  -5.6 8.01e-03    -  1.00e+00 9.99e-01h  1
  46  1.3458847e+00 4.47e-06 6.41e-03  -6.3 8.72e-03    -  1.00e+00 1.00e+00h  1
  47  1.3458476e+00 1.41e-05 1.99e-02  -7.2 7.48e-02    -  1.00e+00 3.14e-01h  1
  48  1.3457672e+00 1.83e-05 9.69e-03  -5.9 4.35e-02    -  1.00e+00 4.87e-01h  1
  49  1.3457238e+00 1.90e-05 7.04e-03  -6.5 2.21e-02    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  50  1.3457234e+00 1.09e-05 1.40e-02  -6.2 3.23e-02    -  1.00e+00 1.00e+00h  1
  51  1.3457135e+00 2.52e-05 1.98e-02  -6.2 5.01e-02    -  1.00e+00 9.10e-01h  1
  52  1.3456795e+00 4.60e-05 1.62e-02  -5.9 3.00e-02    -  1.00e+00 6.80e-01h  1
  53  1.3455965e+00 6.98e-05 2.12e-02  -6.0 2.12e-02    -  1.00e+00 1.00e+00h  1
  54  1.3456745e+00 3.07e-05 5.99e-03  -5.4 2.02e-02    -  1.00e+00 7.15e-01h  1
  55  1.3456732e+00 1.77e-06 2.32e-03  -6.8 1.24e-02    -  1.00e+00 1.00e+00h  1
  56  1.3456570e+00 1.15e-05 9.74e-03  -7.4 1.01e-02    -  1.00e+00 6.53e-01h  1
  57  1.3456578e+00 5.89e-06 2.73e-03  -6.6 3.72e-03    -  1.00e+00 1.00e+00h  1
  58  1.3456565e+00 3.40e-07 5.15e-04  -7.8 6.87e-03    -  1.00e+00 1.00e+00h  1
  59  1.3456490e+00 1.13e-06 3.60e-03  -7.9 8.28e-02    -  1.00e+00 2.57e-01h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  60  1.3456487e+00 1.69e-04 4.34e-02  -5.9 2.46e-01    -  1.00e+00 4.48e-01f  1
  61  1.3455006e+00 1.48e-04 1.15e-02  -6.0 8.46e-02    -  1.00e+00 1.00e+00h  1
  62  1.3460433e+00 1.54e-06 5.02e-02  -5.4 7.28e-02    -  1.00e+00 1.00e+00H  1
  63  1.3454413e+00 1.31e-04 6.32e-03  -5.5 2.87e-02    -  6.27e-01 1.00e+00h  1
  64  1.3456667e+00 2.17e-05 1.42e-02  -5.9 3.44e-02    -  1.00e+00 9.98e-01h  1
  65  1.3456349e+00 2.58e-05 5.25e-03  -6.0 2.68e-02    -  4.90e-01 1.00e+00h  1
  66  1.3457582e+00 1.97e-06 2.10e-02  -5.7 7.57e-02    -  1.00e+00 9.66e-01H  1
  67  1.3456035e+00 3.96e-05 2.65e-03  -5.8 6.48e-02    -  8.64e-01 1.00e+00h  1
  68  1.3456363e+00 8.27e-06 4.84e-03  -6.3 1.93e-02    -  1.00e+00 1.00e+00h  1
  69  1.3456279e+00 7.51e-06 5.31e-03  -6.7 5.41e-03    -  1.00e+00 9.95e-01h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  70  1.3456383e+00 5.31e-06 4.77e-03  -6.4 3.88e-03    -  1.00e+00 1.00e+00h  1
  71  1.3456312e+00 2.41e-06 1.96e-03  -7.1 2.85e-03    -  1.00e+00 1.00e+00h  1
  72  1.3456337e+00 4.45e-07 1.20e-04  -7.3 2.25e-03    -  1.00e+00 9.90e-01h  1
  73  1.3456352e+00 3.29e-11 1.04e-03  -8.8 2.25e-03    -  1.00e+00 1.00e+00H  1
  74  1.3456326e+00 6.53e-07 5.59e-05  -8.0 9.06e-04    -  1.00e+00 1.00e+00h  1
  75  1.3456331e+00 3.41e-09 4.78e-05  -9.9 3.42e-04    -  1.00e+00 1.00e+00h  1
  76  1.3456328e+00 3.42e-08 6.75e-05 -10.4 5.61e-03    -  1.00e+00 4.63e-01h  1
  77  1.3456327e+00 3.89e-08 1.28e-04  -9.2 1.24e-02    -  1.00e+00 3.86e-02h  1
  78  1.3456323e+00 5.95e-07 2.09e-03  -8.4 5.71e-03    -  1.00e+00 7.55e-01h  1
  79  1.3456322e+00 3.31e-07 1.73e-04  -7.9 2.96e-03    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  80  1.3456324e+00 4.85e-07 1.90e-04  -7.6 1.79e-03    -  1.00e+00 1.00e+00h  1
  81  1.3456323e+00 9.27e-08 2.32e-04  -8.6 2.06e-03    -  1.00e+00 9.98e-01h  1
  82  1.3456322e+00 1.81e-06 3.97e-03  -7.7 3.50e-03    -  1.00e+00 1.00e+00h  1
  83  1.3456311e+00 1.16e-06 1.56e-04  -8.1 1.44e-03    -  7.64e-01 1.00e+00h  1
  84  1.3456321e+00 3.29e-09 2.46e-05  -8.8 3.65e-04    -  1.00e+00 1.00e+00h  1
  85  1.3456324e+00 1.27e-07 2.84e-04  -8.0 2.13e-03    -  1.00e+00 1.00e+00h  1
  86  1.3456341e+00 5.14e-10 1.02e-03  -8.1 1.06e-03    -  9.68e-01 1.00e+00H  1
  87  1.3456311e+00 8.34e-07 6.76e-04  -8.1 1.81e-03    -  1.00e+00 1.00e+00h  1
  88  1.3456321e+00 1.64e-08 4.02e-05  -8.1 9.20e-04    -  1.00e+00 1.00e+00h  1
  89  1.3456323e+00 1.63e-11 1.99e-04  -8.4 2.68e-03    -  1.00e+00 1.00e+00H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  90  1.3456329e+00 2.22e-15 5.80e-04  -8.4 2.18e-03    -  1.00e+00 1.00e+00H  1
  91  1.3456321e+00 1.40e-07 3.34e-04  -8.5 3.71e-03    -  8.66e-01 3.33e-01f  1
  92  1.3456317e+00 3.42e-07 1.12e-04  -8.5 1.14e-03    -  7.72e-01 9.64e-01f  1
  93  1.3456317e+00 1.89e-07 7.24e-05  -8.3 1.21e-03    -  1.00e+00 5.00e-01f  2
  94  1.3456384e+00 2.10e-09 2.05e-03  -7.3 2.83e-03    -  1.00e+00 1.00e+00H  1
  95  1.3456296e+00 2.73e-06 2.86e-04  -7.4 2.33e-03    -  1.00e+00 1.00e+00h  1
  96  1.3456318e+00 2.62e-08 6.69e-05  -8.6 4.39e-04    -  1.00e+00 1.00e+00h  1
  97  1.3456318e+00 1.51e-07 1.39e-04 -10.5 7.99e-04    -  1.00e+00 1.00e+00h  1
  98  1.3456317e+00 1.08e-07 2.53e-05  -9.0 8.94e-04    -  1.00e+00 1.00e+00h  1
  99  1.3456317e+00 1.81e-09 4.95e-05 -10.3 7.16e-04    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 100  1.3456317e+00 8.99e-09 6.84e-05 -10.0 8.12e-02    -  1.00e+00 1.51e-02h  1
 101  1.3456314e+00 3.41e-07 1.49e-04  -9.0 2.45e-02    -  1.00e+00 4.85e-01h  1
 102  1.3456371e+00 6.65e-06 6.49e-03  -7.0 3.32e-02    -  8.32e-01 2.58e-01f  1
 103  1.3456277e+00 5.42e-06 1.47e-03  -7.2 1.14e-02    -  1.00e+00 1.00e+00h  1
 104  1.3456360e+00 3.43e-06 2.75e-03  -6.3 1.23e-02    -  1.00e+00 5.86e-01h  1
 105  1.3456380e+00 4.58e-06 4.28e-03  -6.4 4.01e-03    -  1.00e+00 1.00e+00h  1
 106  1.3456375e+00 1.40e-06 1.06e-03  -6.4 7.80e-03    -  1.00e+00 1.00e+00h  1
 107  1.3456410e+00 1.48e-10 4.05e-04  -6.4 8.17e-03    -  1.00e+00 1.00e+00H  1
 108  1.3456476e+00 1.13e-12 7.71e-04  -6.4 3.78e-03    -  1.00e+00 1.00e+00H  1
 109  1.3456337e+00 2.87e-06 4.59e-04  -6.4 7.00e-03    -  1.00e+00 1.00e+00f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 110  1.3456394e+00 1.49e-07 3.41e-04  -6.4 1.15e-03    -  1.00e+00 1.00e+00h  1
 111  1.3456394e+00 1.63e-07 2.16e-04  -6.4 1.05e-03    -  1.00e+00 1.00e+00h  1
 112  1.3456394e+00 1.28e-07 7.53e-05  -6.4 1.88e-03    -  1.00e+00 1.00e+00h  1
 113  1.3456394e+00 7.23e-08 1.14e-04  -6.4 1.10e-03    -  1.00e+00 1.00e+00h  1
 114  1.3456395e+00 2.43e-08 5.01e-05  -6.4 1.05e-03    -  1.00e+00 1.00e+00h  1
 115  1.3456409e+00 9.79e-11 6.43e-04  -6.4 1.62e-03    -  1.00e+00 1.00e+00H  1
 116  1.3456389e+00 3.80e-07 1.69e-05  -6.4 1.42e-03    -  1.00e+00 1.00e+00h  1
 117  1.3456395e+00 1.82e-10 1.33e-05  -6.4 3.40e-04    -  1.00e+00 1.00e+00h  1
 118  1.3456398e+00 2.74e-11 2.05e-04  -6.4 4.61e-03    -  1.00e+00 1.00e+00H  1
 119  1.3456397e+00 3.33e-15 2.12e-04  -6.4 7.05e-03    -  1.00e+00 1.00e+00H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 120  1.3456397e+00 1.10e-11 1.70e-04  -6.4 1.99e-02    -  1.00e+00 1.95e-03h 10
 121  1.3456726e+00 1.33e-15 2.37e-03  -6.4 5.90e-02    -  1.00e+00 1.00e+00H  1
 122  1.3456275e+00 1.44e-05 4.05e-03  -6.4 3.37e-02    -  1.00e+00 1.00e+00f  1
 123  1.3456515e+00 7.86e-05 1.58e-02  -5.7 9.35e-02    -  1.00e+00 7.40e-01h  1
 124  1.3455411e+00 9.08e-05 1.22e-02  -5.8 4.95e-02    -  1.00e+00 1.00e+00h  1
 125  1.3456452e+00 2.03e-04 3.64e-02  -5.1 1.12e-01    -  1.00e+00 3.98e-01h  2
 126  1.3455475e+00 1.40e-04 9.16e-03  -5.2 3.00e-02    -  8.76e-01 1.00e+00h  1
 127  1.3457256e+00 1.08e-05 8.21e-03  -5.2 1.51e-02    -  1.00e+00 1.00e+00h  1
 128  1.3457456e+00 4.70e-06 3.24e-03  -5.2 1.58e-02    -  1.00e+00 1.00e+00h  1
 129  1.3457655e+00 5.04e-09 1.01e-03  -5.2 1.31e-02    -  1.00e+00 1.00e+00H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 130  1.3457402e+00 6.65e-06 5.30e-03  -5.2 1.28e-02    -  1.00e+00 1.00e+00h  1
 131  1.3458002e+00 2.61e-11 2.26e-03  -5.2 2.13e-02    -  1.00e+00 1.00e+00H  1
 132  1.3457151e+00 2.29e-05 7.63e-04  -5.2 1.73e-02    -  1.00e+00 1.00e+00f  1
 133  1.3457513e+00 3.74e-07 4.60e-04  -5.2 1.46e-03    -  1.00e+00 1.00e+00h  1
 134  1.3457518e+00 2.11e-07 7.18e-05  -5.2 1.15e-03    -  1.00e+00 1.00e+00h  1
 135  1.3457518e+00 7.04e-08 1.14e-04  -5.2 1.06e-03    -  1.00e+00 1.00e+00h  1
 136  1.3457503e+00 9.90e-08 1.63e-04  -5.2 2.42e-03    -  1.00e+00 1.00e+00h  1
 137  1.3457509e+00 6.56e-07 1.87e-03  -5.2 1.09e-02    -  1.00e+00 1.00e+00h  1
 138  1.3457541e+00 3.85e-07 1.29e-04  -5.2 2.63e-03    -  1.00e+00 1.00e+00h  1
 139  1.3457497e+00 3.39e-07 1.22e-04  -5.2 1.81e-03    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 140  1.3457515e+00 2.21e-07 6.18e-05  -5.2 2.48e-03    -  1.00e+00 1.00e+00h  1
 141  1.3457527e+00 2.36e-07 3.16e-04  -5.2 1.24e-03    -  1.00e+00 1.00e+00h  1
 142  1.3457526e+00 2.19e-07 1.66e-04  -5.2 1.84e-03    -  1.00e+00 1.00e+00h  1
 143  1.3457491e+00 7.06e-07 1.86e-03  -5.2 2.06e-03    -  1.00e+00 1.00e+00h  1
 144  1.3457518e+00 5.62e-07 1.61e-04  -5.2 9.80e-04    -  1.00e+00 1.00e+00h  1
 145  1.3457522e+00 3.54e-07 1.66e-04  -5.2 1.24e-03    -  1.00e+00 5.00e-01h  2
 146  1.3457520e+00 1.66e-08 1.57e-05  -5.2 3.12e-04    -  1.00e+00 1.00e+00h  1
 147  1.3456452e+00 4.70e-06 4.78e-03  -7.0 7.90e-03    -  9.61e-01 1.00e+00h  1
 148  1.3456311e+00 3.94e-06 3.76e-03  -7.0 1.50e-02    -  1.00e+00 1.00e+00h  1
 149  1.3456301e+00 3.56e-06 5.13e-03  -7.0 1.19e-02    -  1.00e+00 1.60e-01h  2
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 150  1.3456327e+00 7.85e-07 1.76e-03  -7.0 2.49e-03    -  1.00e+00 1.00e+00h  1
 151  1.3456336e+00 1.04e-07 8.21e-05  -7.0 8.93e-04    -  1.00e+00 9.26e-01h  1
 152  1.3456336e+00 1.27e-06 3.28e-03  -7.0 3.11e-03    -  1.00e+00 1.00e+00f  1
 153  1.3456328e+00 8.89e-07 1.19e-03  -7.0 8.91e-04    -  1.00e+00 1.00e+00h  1
 154  1.3456336e+00 2.82e-08 6.42e-05  -7.0 4.29e-04    -  1.00e+00 1.00e+00h  1
 155  1.3456335e+00 3.61e-09 3.02e-05  -7.0 5.40e-04    -  1.00e+00 1.00e+00h  1
 156  1.3456332e+00 3.04e-08 1.09e-04  -7.0 2.98e-03    -  1.00e+00 1.00e+00h  1
 157  1.3456355e+00 1.17e-10 5.28e-04  -7.0 7.62e-03    -  1.00e+00 1.00e+00H  1
 158  1.3456309e+00 1.44e-06 1.64e-03  -7.0 4.30e-03    -  1.00e+00 1.00e+00h  1
 159  1.3456465e+00 6.88e-09 1.94e-03  -7.2 8.88e-03    -  1.00e+00 1.00e+00H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 160  1.3456213e+00 6.97e-06 2.62e-04  -7.3 8.48e-03    -  1.00e+00 1.00e+00h  1
 161  1.3456315e+00 5.26e-08 2.22e-04  -8.5 1.66e-03    -  1.00e+00 1.00e+00h  1
 162  1.3456314e+00 1.98e-07 9.06e-05  -9.7 1.60e-03    -  1.00e+00 1.00e+00h  1
 163  1.3456314e+00 6.97e-08 3.72e-05  -8.5 1.18e-03    -  1.00e+00 1.00e+00h  1
 164  1.3456316e+00 2.42e-08 8.90e-05  -8.5 2.23e-03    -  1.00e+00 8.61e-01H  1
 165  1.3456314e+00 7.07e-08 5.50e-05  -9.5 6.38e-04    -  1.00e+00 1.00e+00h  1
 166  1.3456314e+00 1.40e-07 2.44e-04  -8.6 9.32e-04    -  1.00e+00 1.00e+00h  1
 167  1.3456313e+00 9.02e-08 5.44e-05  -8.7 5.93e-04    -  1.00e+00 1.00e+00h  1
 168  1.3456314e+00 3.18e-08 7.92e-05 -10.4 6.73e-04    -  1.00e+00 1.00e+00h  1
 169  1.3456314e+00 2.47e-08 5.93e-05 -11.0 2.57e-04    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 170  1.3456315e+00 2.89e-12 2.77e-04  -9.7 8.23e-04    -  1.00e+00 1.00e+00H  1
 171  1.3456313e+00 3.80e-08 7.24e-06 -11.0 6.85e-04    -  1.00e+00 1.00e+00h  1
 172  1.3456314e+00 5.51e-11 7.82e-06 -11.0 6.90e-05    -  1.00e+00 1.00e+00h  1
 173  1.3456314e+00 6.22e-10 1.10e-05 -11.0 3.27e-03    -  1.00e+00 6.96e-02h  1
 174  1.3456314e+00 2.07e-07 3.62e-04 -11.0 5.82e-03    -  1.00e+00 6.27e-01h  1
 175  1.3456310e+00 3.95e-07 2.69e-04 -11.0 1.24e-03    -  7.54e-01 1.00e+00h  1
 176  1.3456310e+00 3.87e-07 2.40e-04 -11.0 1.87e-03    -  3.94e-01 2.06e-02h  1
 177  1.3456309e+00 2.05e-06 2.64e-03 -10.8 4.11e-03    -  1.00e+00 1.00e+00h  1
 178  1.3456294e+00 1.63e-06 9.35e-04 -10.8 2.73e-03    -  5.04e-01 1.00e+00h  1
 179  1.3456336e+00 4.19e-10 7.27e-04  -9.4 5.79e-03    -  1.00e+00 1.00e+00H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 180  1.3456294e+00 1.07e-06 2.72e-04  -9.5 3.34e-03    -  9.85e-01 1.00e+00h  1
 181  1.3456314e+00 1.70e-08 2.03e-05 -10.0 6.09e-04    -  1.00e+00 1.00e+00h  1
 182  1.3456314e+00 3.86e-13 9.96e-05  -9.2 1.45e-03    -  1.00e+00 1.00e+00H  1
 183  1.3456377e+00 4.81e-13 1.44e-03  -9.3 5.01e-03    -  4.09e-01 1.00e+00H  1
 184  1.3456265e+00 3.53e-06 1.61e-04  -9.3 5.74e-03    -  1.00e+00 1.00e+00f  1
 185  1.3456314e+00 6.70e-09 4.97e-05 -10.4 1.62e-04    -  1.00e+00 1.00e+00h  1
 186  1.3456314e+00 4.65e-09 2.81e-05 -11.0 2.55e-04    -  1.00e+00 1.00e+00h  1
 187  1.3456314e+00 1.60e-14 2.46e-05 -11.0 1.81e-04    -  1.00e+00 1.00e+00H  1
 188  1.3456313e+00 3.89e-09 8.43e-06 -11.0 3.69e-04    -  1.00e+00 1.00e+00h  1
 189  1.3456314e+00 3.88e-13 2.96e-05 -11.0 4.90e-04    -  1.00e+00 1.00e+00H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 190  1.3456313e+00 6.68e-09 7.18e-06 -11.0 3.69e-04    -  1.00e+00 1.00e+00h  1
 191  1.3456314e+00 3.92e-09 4.98e-05 -11.0 1.55e-04    -  1.00e+00 1.00e+00h  1
 192  1.3456313e+00 2.79e-09 4.93e-06 -11.0 1.27e-04    -  1.00e+00 1.00e+00h  1
 193  1.3456314e+00 2.89e-11 3.07e-06 -11.0 6.65e-05    -  1.00e+00 1.00e+00h  1
 194  1.3456314e+00 3.85e-08 1.89e-04  -9.7 2.53e-02    -  1.00e+00 4.02e-02h  2
 195  1.3456314e+00 3.13e-08 8.15e-05  -9.9 2.35e-03    -  1.00e+00 4.34e-01h  1
 196  1.3456309e+00 1.15e-06 2.22e-03  -9.9 1.57e-03    -  3.34e-01 1.00e+00f  1
 197  1.3456304e+00 7.91e-07 8.53e-05 -10.3 1.41e-03    -  1.00e+00 1.00e+00h  1
 198  1.3456313e+00 9.79e-10 1.48e-05 -11.0 1.36e-04    -  1.00e+00 1.00e+00h  1
 199  1.3456313e+00 7.57e-10 9.47e-06 -10.2 6.91e-04    -  1.00e+00 3.99e-01h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 200  1.3456313e+00 1.33e-07 1.23e-04 -10.8 3.13e-03    -  1.00e+00 1.00e+00h  1
 201  1.3456311e+00 1.14e-07 5.23e-05  -8.8 2.99e-03    -  5.87e-01 1.00e+00h  1
 202  1.3456320e+00 7.51e-07 1.38e-03  -7.2 7.47e-02    -  1.00e+00 1.43e-01h  1
 203  1.3456309e+00 1.86e-06 2.64e-03  -7.3 9.53e-03    -  9.11e-01 1.00e+00h  1
 204  1.3456308e+00 2.93e-06 2.58e-03  -7.3 1.77e-02    -  4.19e-01 1.09e-01h  4
 205  1.3456307e+00 8.81e-07 6.01e-04  -7.3 7.74e-03    -  1.00e+00 1.00e+00h  1
 206  1.3456378e+00 1.45e-10 1.32e-03  -7.3 1.04e-02    -  1.00e+00 1.00e+00H  1
 207  1.3456313e+00 1.29e-06 1.41e-03  -7.3 7.75e-03    -  1.00e+00 1.00e+00h  1
 208  1.3456296e+00 2.13e-06 2.03e-03  -7.3 1.92e-02    -  7.85e-01 5.31e-01h  1
 209  1.3456304e+00 1.25e-06 1.75e-03  -7.3 7.97e-03    -  1.00e+00 5.00e-01f  2
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 210  1.3456271e+00 1.03e-05 8.58e-03  -7.3 1.73e-02    -  1.00e+00 9.58e-01h  1
 211  1.3456178e+00 2.44e-05 9.66e-03  -7.3 9.94e-03    -  6.77e-01 1.00e+00f  1
 212  1.3456469e+00 3.23e-05 1.63e-02  -6.2 1.56e-02    -  1.00e+00 9.85e-01h  1
 213  1.3455897e+00 4.49e-05 1.03e-02  -6.2 2.37e-02    -  8.53e-01 1.00e+00h  1
 214  1.3456430e+00 3.12e-05 1.90e-02  -6.2 1.51e-02    -  1.00e+00 9.74e-01h  1
 215  1.3456140e+00 2.08e-05 4.74e-03  -6.3 1.48e-02    -  3.60e-01 6.03e-01h  1
 216  1.3456147e+00 1.84e-05 3.69e-03  -6.9 7.67e-03    -  1.00e+00 1.25e-01f  4
 217  1.3456313e+00 1.68e-06 7.73e-04  -7.0 2.65e-03    -  1.00e+00 1.00e+00h  1
 218  1.3456331e+00 1.82e-08 5.86e-05  -7.1 3.63e-04    -  1.00e+00 1.00e+00h  1
 219  1.3456329e+00 8.61e-08 3.16e-04  -7.1 9.74e-04    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 220  1.3456328e+00 2.17e-07 2.53e-04  -7.1 9.48e-04    -  1.00e+00 1.00e+00h  1
 221  1.3456327e+00 1.09e-07 7.00e-05  -7.1 1.39e-03    -  1.00e+00 1.00e+00h  1
 222  1.3456328e+00 1.48e-08 1.83e-05  -7.1 4.30e-04    -  1.00e+00 1.00e+00h  1
 223  1.3456329e+00 2.61e-09 1.28e-05  -7.1 4.28e-04    -  1.00e+00 1.00e+00h  1
 224  1.3456329e+00 1.25e-08 7.90e-05  -7.1 1.01e-03    -  1.00e+00 1.00e+00h  1
 225  1.3456350e+00 3.47e-10 8.50e-04  -7.1 5.20e-03    -  1.00e+00 1.00e+00H  1
 226  1.3456315e+00 1.14e-06 8.80e-04  -7.1 3.78e-03    -  1.00e+00 1.00e+00h  1
 227  1.3456317e+00 1.22e-06 1.65e-03  -7.1 8.26e-03    -  1.00e+00 4.93e-01h  2
 228  1.3456327e+00 4.48e-07 1.79e-03  -7.1 5.05e-03    -  1.00e+00 1.00e+00h  1
 229  1.3456321e+00 6.01e-07 1.10e-03  -7.1 1.40e-02    -  1.00e+00 1.85e-01h  2
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 230  1.3456324e+00 2.39e-07 5.78e-05  -7.1 2.35e-03    -  1.00e+00 1.00e+00h  1
 231  1.3456329e+00 6.91e-08 1.60e-04  -7.1 5.10e-04    -  1.00e+00 1.00e+00h  1
 232  1.3456328e+00 7.51e-08 8.23e-05  -7.1 1.71e-03    -  1.00e+00 1.00e+00h  1
 233  1.3456351e+00 1.02e-10 7.73e-04  -7.1 4.30e-03    -  1.00e+00 1.00e+00H  1
 234  1.3456308e+00 2.07e-06 1.03e-03  -7.1 1.41e-03    -  1.00e+00 1.00e+00h  1
 235  1.3456327e+00 9.04e-08 2.05e-04  -7.1 1.45e-03    -  1.00e+00 1.00e+00h  1
 236  1.3456328e+00 3.20e-08 4.66e-05  -7.1 1.09e-03    -  1.00e+00 1.00e+00h  1
 237  1.3456329e+00 2.21e-12 7.33e-05  -7.1 5.18e-04    -  1.00e+00 1.00e+00H  1
 238  1.3456328e+00 3.31e-08 6.11e-05  -7.1 1.22e-03    -  1.00e+00 1.00e+00h  1
 239  1.3456328e+00 2.59e-08 5.80e-05  -7.1 3.95e-04    -  1.00e+00 5.00e-01h  2
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 240  1.3456328e+00 1.22e-08 2.39e-05  -7.1 8.11e-04    -  1.00e+00 1.00e+00h  1
 241  1.3456333e+00 6.22e-15 2.83e-04  -7.1 1.10e-03    -  1.00e+00 1.00e+00H  1
 242  1.3456325e+00 2.84e-07 2.77e-05  -7.1 1.21e-03    -  1.00e+00 1.00e+00f  1
 243  1.3456328e+00 5.22e-09 6.16e-05  -7.1 1.95e-04    -  1.00e+00 1.00e+00h  1
 244  1.3456328e+00 2.41e-09 2.48e-06  -7.1 1.48e-04    -  1.00e+00 1.00e+00h  1
 245  1.3456328e+00 1.01e-11 2.39e-06  -7.1 1.53e-05    -  1.00e+00 1.00e+00h  1
 246  1.3456329e+00 1.15e-13 8.84e-05  -7.1 8.66e-04    -  1.00e+00 1.00e+00H  1
 247  1.3456329e+00 1.33e-15 6.96e-05  -7.1 7.45e-04    -  1.00e+00 1.00e+00H  1
 248  1.3456327e+00 1.04e-07 6.95e-05  -7.1 1.83e-03    -  1.00e+00 1.00e+00f  1
 249  1.3456327e+00 7.58e-08 7.63e-05  -7.1 1.15e-03    -  1.00e+00 1.00e+00h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 250  1.3456331e+00 6.66e-16 2.21e-04  -7.1 6.70e-04    -  1.00e+00 1.00e+00H  1
 251  1.3456329e+00 1.78e-15 1.69e-04  -7.1 5.62e-04    -  1.00e+00 1.00e+00F  1
 252  1.3456328e+00 2.97e-08 5.73e-05  -7.1 6.86e-04    -  1.00e+00 1.00e+00h  1
 253  1.3456328e+00 2.67e-09 2.65e-05  -7.1 5.33e-05    -  1.00e+00 1.00e+00h  1
 254  1.3456328e+00 6.69e-10 3.99e-06  -7.1 4.29e-05    -  1.00e+00 1.00e+00h  1
 255  1.3456328e+00 5.19e-11 1.69e-06  -7.1 1.17e-05    -  1.00e+00 1.00e+00h  1
 256  1.3456328e+00 7.80e-11 3.92e-06  -7.1 2.46e-05    -  1.00e+00 1.00e+00h  1
 257  1.3456328e+00 1.00e-10 3.40e-06  -7.1 6.55e-05    -  1.00e+00 1.00e+00h  1
 258  1.3456328e+00 2.10e-10 6.36e-06  -7.1 1.15e-04    -  1.00e+00 1.00e+00h  1
 259  1.3456328e+00 6.91e-14 4.64e-05  -7.1 3.88e-04    -  1.00e+00 1.00e+00H  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 260  1.3456328e+00 4.77e-09 9.32e-06  -7.1 2.80e-04    -  1.00e+00 1.00e+00h  1
 261  1.3456328e+00 1.11e-09 1.62e-05  -7.1 1.16e-04    -  1.00e+00 1.00e+00h  1
 262  1.3456329e+00 1.33e-15 7.27e-05  -7.1 4.27e-04    -  1.00e+00 1.00e+00H  1
 263  1.3456328e+00 9.59e-09 1.45e-06  -7.1 3.99e-04    -  1.00e+00 1.00e+00h  1
 264  1.3456328e+00 2.16e-11 2.10e-06  -7.1 1.51e-05    -  1.00e+00 1.00e+00h  1
 265  1.3456328e+00 2.89e-15 2.01e-05  -7.1 2.70e-04    -  1.00e+00 1.00e+00H  1
 266  1.3456328e+00 7.30e-10 1.44e-05  -7.1 2.48e-03    -  1.00e+00 2.50e-01h  3
 267  1.3456352e+00 1.11e-15 4.19e-04  -7.1 9.50e-03    -  1.00e+00 1.00e+00H  1
 268  1.3456329e+00 6.66e-16 1.13e-04  -7.1 8.57e-03    -  1.00e+00 1.00e+00F  1
 269  1.3456328e+00 3.97e-08 5.10e-05  -7.1 5.61e-02    -  6.53e-01 3.12e-02f  6
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 270  1.3456328e+00 2.69e-08 4.81e-05  -7.1 1.25e-03    -  1.00e+00 5.00e-01h  2
 271  1.3456329e+00 4.94e-12 1.15e-04  -7.1 1.03e-03    -  1.00e+00 1.00e+00H  1
 272  1.3456329e+00 1.77e-12 1.11e-04  -7.1 1.05e-03    -  1.00e+00 1.00e+00H  1
 273  1.3456369e+00 1.89e-14 7.74e-04  -7.1 2.99e-03    -  1.00e+00 1.00e+00H  1
 274  1.3456305e+00 1.57e-06 4.96e-05  -7.1 2.77e-03    -  1.00e+00 1.00e+00f  1
 275  1.3456328e+00 1.98e-10 4.69e-06  -7.1 8.23e-05    -  1.00e+00 1.00e+00h  1
 276  1.3456328e+00 3.80e-14 5.84e-05  -7.1 2.47e-04    -  1.00e+00 1.00e+00H  1
 277  1.3456328e+00 4.25e-09 2.86e-06  -7.1 2.42e-04    -  1.00e+00 1.00e+00h  1
 278  1.3456328e+00 2.27e-09 7.96e-06  -7.1 1.14e-04    -  1.00e+00 5.00e-01h  2
 279  1.3456328e+00 1.17e-09 1.49e-06  -7.1 5.27e-05    -  1.00e+00 5.00e-01h  2
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
 280  1.3456328e+00 7.92e-10 1.17e-05  -7.1 1.78e-04    -  1.00e+00 1.00e+00h  1
 281  1.3456329e+00 4.44e-16 1.13e-04  -7.1 2.41e-04    -  1.00e+00 1.00e+00H  1
 282  1.3456328e+00 1.54e-08 1.71e-06  -7.1 3.63e-04    -  1.00e+00 1.00e+00h  1
 283  1.3456328e+00 7.91e-12 6.49e-07  -7.1 1.40e-05    -  1.00e+00 1.00e+00h  1

Number of Iterations....: 283

                                   (scaled)                 (unscaled)
Objective...............:   1.3456328267214988e+00    1.3456328267214988e+00
Dual infeasibility......:   6.4915668204113537e-07    6.4915668204113537e-07
Constraint violation....:   7.9141138087379659e-12    7.9141138087379659e-12
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   8.3249267374269510e-08    8.3249267374269510e-08
Overall NLP error.......:   6.4915668204113537e-07    6.4915668204113537e-07


Number of objective function evaluations             = 413
Number of objective gradient evaluations             = 283
Number of equality constraint evaluations            = 413
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 285
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 0
Total seconds in IPOPT                               = 48.718

EXIT: Optimal Solution Found.

Reconstruct the optimized parameters and plot the trajectory.

_, reconstruct_ms = pack(default_vectorizer(), ms_dynprob.ps)
optimized_parameters = reconstruct_ms(ms_uopt.u)
ms_optsol, _ = mslayer(nothing, optimized_parameters, ms_opt.p)
trajectoryplot(ms_optsol)

Trajectory plot for The Lotka Volterra Fishing Problem

Matching residuals measure feasibility of the lifted states and inserted control intervals. The single- and multiple-shooting problems use different control grids, and this multiple-shooting model also bounds its lifted states (including the quadrature) by two. Their objective values need not coincide.

maximum(abs, shooting_constraints(ms_optsol))
7.914113808737966e-12

Appendix

This example was built using these direct dependencies,
        using Pkg
        Pkg.status()
Status `~/work/Corleone.jl/Corleone.jl/docs/Project.toml`
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and using this machine and Julia version.
        using InteractiveUtils
        InteractiveUtils.versioninfo()
Julia Version 1.13.3
Commit 67ac47b9cd8 (2026-10-25 15:28 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
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  CPU: 4 × AMD EPYC 7763 64-Core Processor
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  LLVM: libLLVM-20.1.8 (ORCJIT, znver3)
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Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)
A more complete overview of all dependencies and their versions is also provided.
        using Pkg
        Pkg.status(; mode = PKGMODE_MANIFEST)
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  [1317d2d5] oneTBB_jll v2023.1.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
⌅ [dfaa095f] x265_jll v4.1.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [8bf52ea8] CRC32c v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.7.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v1.0.0
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.13.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.13.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v1.0.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.13.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.5.5+2
  [deac9b47] LibCURL_jll v8.22.0+0
  [e37daf67] LibGit2_jll v1.9.7+0
  [29816b5a] LibSSH2_jll v1.11.104+0
  [14a3606d] MozillaCACerts_jll v2026.10.20
  [4536629a] OpenBLAS_jll v0.3.30+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.8+0
  [efcefdf7] PCRE2_jll v10.47.0+0
  [bea87d4a] SuiteSparse_jll v7.10.1+0
  [83775a58] Zlib_jll v1.3.2+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.70.0+0
  [3f19e933] p7zip_jll v17.8.3+0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

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