Outputs
Our solver returns a GenericExecutionStats object, defined in SolverCore.jl. This section describes the fields of that object populated by Penelopt.jl, as well as the console output produced when print_level > 0.
julia> stats = L2Penalty(nlp)The GenericExecutionStats Object
stats.status::Symbol: exit status of the algorithm. See Status below for the list of possible values.stats.solution::V: the final iterate $x_k$.stats.objective::T: the value of $f(x_k)$ at the final iterate.stats.primal_feas::T: the primal feasibility measure $\lVert c(x_k) \rVert_{\infty}$.stats.dual_feas::T: the dual feasibility measure $\lVert \nabla f(x_k) + J(x_k)^T y_k \rVert_{\infty}$.stats.multipliers::V: the vector of Lagrange multiplier estimates $y_k$ at the final iterate.stats.iter::Int: the number of (outer) iterations performed.stats.elapsed_time::Float64: total elapsed (CPU) time, in seconds.stats.solver_specific::Dict{Symbol,T}: a dictionary of algorithm-specific quantities, described next.
solver_specific Entries
:n_fact::Int: the cumulative number of matrix factorizations performed by the linear solver over the whole solve.
Status
stats.status can take one of the following values:
| Status | Meaning |
|---|---|
:first_order | A first-order stationary point was found within tolerance. |
:infeasible | The problem was declared locally infeasible: see infeasible_tol and infeasible_iter in the options. |
:unbounded | The objective appears to be unbounded below. |
:not_desc | The Moré–Sorensen subsolver could not compute a descent step; see ms_accept_descent. |
:small_step | The computed step was numerically insignificant; see r2n_tiny_step_tol. |
:max_iter | The iteration limit max_iter was reached. |
:max_time | The time limit max_time was reached. |
:max_eval | The objective evaluation limit max_eval was reached. |
:exception | An internal exception occurred (e.g., the regularization parameter exceeded ms_σmax). |
:unknown | The algorithm has not (yet) satisfied any stopping criterion; this should not appear in a returned stats object. |
A :infeasible status means the algorithm detected apparent local infeasibility using the heuristic described by infeasible_tol; it is not a certificate of infeasibility.
Console Output
Setting the keyword argument print_level to a value $\geq 1$ turns on console logging. Because the solver is organized as nested loops (see terminology), print_level also controls how deep the logging goes:
print_level | Loops logged |
|---|---|
0 | none (default) |
1 | outer (penalty) loop |
2 | outer + R2N loop |
3 | outer + R2N + Moré–Sorensen loop |
The frequency (in iterations) at which each loop prints a line is controlled independently by verbose, r2n_verbose, and ms_verbose. Additionally, when print_level ≥ 1, the solver prints an introduction message at the start of the solve, describing the problem and the solver configuration.
If you set the linear_solver option and want to confirm it is actually being used, run with print_level ≥ 1: the introduction message printed at the start of the solve reports the linear solver library in use.
Outer-Loop Header
For the outer loop logger, the logger prints the following columns:
Iter: outer iteration counter.sIter: number of R2N (inner) iterations performed to solve the current penalized subproblem.Objective: current value of $f(x_k)$.pfeas: primal feasibility $\lVert c(x_k) \rVert_{\infty}$.dfeas: dual feasibility $\lVert \nabla f(x_k) + J(x_k)^Ty_k \rVert_{\infty}$.τ: current penalty parameter.ptol: primal feasibility tolerance for the current subproblem ($\epsilon^P_k$).dtol: dual feasibility tolerance for the current subproblem ($\epsilon^D_k$).‖x‖: norm of the current iterate.
For example,
using CUTEst, Penelopt
nlp = CUTEstModel("BT7")
stats = L2Penalty(nlp; print_level = 1)┌ Info:
│ This is Penelopt.jl v0.1.0.
│ Running with linear solver LDLFactorizations.jl v0.10.2.
│
│ Problem name: BT7
│ All variables: ████████████████████ 5 All constraints: ████████████████████ 3
│ free: ████████████████████ 5 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 fixed: ████████████████████ 3
│ infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ nnzh: ( 60.00% sparsity) 6 linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ nonlinear: ████████████████████ 3
│ nnzj: ( 46.67% sparsity) 8
│ lin_nnzj: (------% sparsity)
│ nln_nnzj: ( 46.67% sparsity) 8
│
└
[ Info: ------------------------------------------------------------------------------------------------------
[ Info: Iter sIter Objective pfeas dfeas τ ptol dtol ‖x‖
[ Info: ------------------------------------------------------------------------------------------------------
[ Info: 0 0 +9.0900000e+02 3.44e+03 4.00e+00 1.03e+03 1.00e+00 1.00e+00 2.83e+00
[ Info: 1 11 +1.5087784e+02 1.02e-01 3.29e-01 1.03e+03 1.02e-03 3.29e-03 2.45e+00
[ Info: 2 2 +1.5121076e+02 1.01e-01 2.08e-05 1.36e+03 1.02e-03 5.12e-05 2.67e+00
[ Info: 3 2 +2.1212673e+02 5.43e-02 1.23e-03 1.78e+03 1.02e-03 5.12e-05 2.92e+00
[ Info: 4 2 +3.0650000e+02 3.26e-09 8.36e-05 1.78e+03 7.45e-08 5.12e-05 2.96e+00
[ Info: 5 1 +3.0650000e+02 3.89e-13 1.32e-11 1.78e+03 7.45e-08 5.12e-05 2.96e+00
┌ Info:
│ Number of Iterations: 5
│
│
│ Objective...........: +3.064999999992104e+02
│ Primal Feasibility..: 3.888001032237298e-13
│ Dual Feasibility....: 1.322953281763465e-11
│
│
└ EXIT: first_order.Inner (R2N)-Loop Header
For the inner loop logger, the logger prints the following columns:
Iter: R2N iteration counter (within the current penalized subproblem).sIter: number of Moré–Sorensen iterations used to compute the current step.Objective: current value of the penalized objective $f(x) + \tau_k \lVert c(x) \rVert_2$.pfeas,dfeas: as above.σ: current R2N quadratic regularization parameter.ρ: ratio of actual to first-order predicted decrease for the last step.‖x‖: norm of the current inner iterate.‖s‖: norm of the last computed step.
For example,
using CUTEst, Penelopt
nlp = CUTEstModel("BT7")
stats = L2Penalty(nlp; print_level = 2)┌ Info:
│ This is Penelopt.jl v0.1.0.
│ Running with linear solver LDLFactorizations.jl v0.10.2.
│
│ Problem name: BT7
│ All variables: ████████████████████ 5 All constraints: ████████████████████ 3
│ free: ████████████████████ 5 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 fixed: ████████████████████ 3
│ infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ nnzh: ( 60.00% sparsity) 6 linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ nonlinear: ████████████████████ 3
│ nnzj: ( 46.67% sparsity) 8
│ lin_nnzj: (------% sparsity)
│ nln_nnzj: ( 46.67% sparsity) 8
│
└
[ Info: ------------------------------------------------------------------------------------------------------
[ Info: Iter sIter Objective pfeas dfeas τ ptol dtol ‖x‖
[ Info: ------------------------------------------------------------------------------------------------------
[ Info: 0 0 +9.0900000e+02 3.44e+03 4.00e+00 1.03e+03 1.00e+00 1.00e+00 2.83e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.03e+03 ‖c(x)‖₂ with tolerance 1.00e+00...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +5.7728911e+03 Inf Inf 2.22e-16 +0.00e+00 2.83e+00 1.39e-309
[ Info: | 1 0 +4.6709605e+03 4.00e+00 1.37e+03 7.40e+01 +1.83e-01 2.87e+00 2.30e+00
[ Info: | 2 0 +2.9029691e+03 4.37e+00 7.70e+02 2.47e+02 +3.72e-01 2.30e+00 1.71e+00
[ Info: | 3 0 +1.7076691e+03 2.80e+00 3.82e+02 8.22e+01 +6.23e-01 1.46e+00 1.63e+00
[ Info: | 4 0 +1.3012830e+03 1.63e+00 5.80e+02 2.74e+01 +7.27e-01 7.69e-01 1.51e+00
[ Info: | 5 0 +2.9219305e+03 1.07e+00 3.41e+02 9.14e+00 +3.64e-01 2.35e+00 2.32e+00
[ Info: | 6 1 +3.3219848e+02 2.64e+00 6.26e+03 3.05e+03 +1.01e+00 2.34e+00 5.64e-01
[ Info: | 7 1 +2.7243130e+02 1.72e-01 3.79e+03 1.02e+03 +1.00e+00 2.36e+00 5.56e-02
[ Info: | 8 1 +2.6756062e+02 1.37e-01 1.06e+02 3.38e+02 +1.00e+00 2.38e+00 5.99e-02
[ Info: | 9 1 +2.6538496e+02 1.21e-01 4.71e+01 1.13e+02 +1.00e+00 2.41e+00 5.82e-02
[ Info: | 10 1 +2.6494735e+02 1.10e-01 1.37e+01 3.76e+01 +1.00e+00 2.44e+00 3.64e-02
[ Info: | 11 1 +2.6492031e+02 1.04e-01 3.01e+00 1.25e+01 +1.00e+00 2.45e+00 1.13e-02
┌ Info: |
│ | Subproblem solved with status first_order after 11 iterations.
│ | Reached dfeas = 0.32948563926746943
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 1 11 +1.5087784e+02 1.02e-01 3.29e-01 1.03e+03 1.02e-03 3.29e-03 2.45e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.03e+03 ‖c(x)‖₂ with tolerance 3.29e-03...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +2.6492031e+02 0.00e+00 3.29e-01 1.25e+01 +0.00e+00 2.45e+00 1.13e-02
[ Info: | 1 1 +2.6492001e+02 1.02e-01 3.29e-01 4.18e+00 +1.00e+00 2.45e+00 1.36e-03
[ Info: | 2 2 +2.6492001e+02 1.01e-01 1.30e-02 1.39e+00 +1.00e+00 2.45e+00 6.91e-06
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 2.078326150973622e-5
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 2 2 +1.5121076e+02 1.01e-01 2.08e-05 1.36e+03 1.02e-03 5.12e-05 2.67e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.36e+03 ‖c(x)‖₂ with tolerance 5.12e-05...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 2 +2.9459842e+02 0.00e+00 2.08e-05 1.39e+00 +0.00e+00 2.67e+00 6.91e-06
[ Info: | 1 1 +2.9193260e+02 4.66e-02 1.03e+02 4.64e-01 +1.00e+00 2.66e+00 1.98e-02
[ Info: | 2 1 +2.9193044e+02 5.49e-02 1.89e+00 1.55e-01 +1.00e+00 2.66e+00 3.58e-03
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 0.001227789363797617
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 3 2 +2.1212673e+02 5.43e-02 1.23e-03 1.78e+03 1.02e-03 5.12e-05 2.92e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.78e+03 ‖c(x)‖₂ with tolerance 5.12e-05...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +3.2390866e+02 0.00e+00 1.23e-03 1.55e-01 +0.00e+00 2.92e+00 3.58e-03
[ Info: | 1 0 +3.0658010e+02 1.16e-02 1.31e+02 5.16e-02 +1.00e+00 2.96e+00 4.20e-02
[ Info: | 2 0 +3.0650001e+02 5.82e-05 5.08e+00 1.72e-02 +1.00e+00 2.96e+00 1.54e-04
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 8.363531196664553e-5
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 4 2 +3.0650000e+02 3.26e-09 8.36e-05 1.78e+03 7.45e-08 5.12e-05 2.96e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.78e+03 ‖c(x)‖₂ with tolerance 5.12e-05...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +3.0650001e+02 0.00e+00 8.36e-05 1.72e-02 +0.00e+00 2.96e+00 1.54e-04
[ Info: | 1 0 +3.0650000e+02 3.26e-09 8.36e-05 5.73e-03 +1.00e+00 2.96e+00 7.70e-10
┌ Info: |
│ | Subproblem solved with status first_order after 1 iterations.
│ | Reached dfeas = 1.3229532817634647e-11
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 5 1 +3.0650000e+02 3.89e-13 1.32e-11 1.78e+03 7.45e-08 5.12e-05 2.96e+00
┌ Info:
│ Number of Iterations: 5
│
│
│ Objective...........: +3.064999999992104e+02
│ Primal Feasibility..: 3.888001032237298e-13
│ Dual Feasibility....: 1.322953281763465e-11
│
│
└ EXIT: first_order.MS-Loop Header
Using print_level = 3 prints out a lot of information (you are printing 3 nested loops), as you will see below. We recommend to use print_level < 3 first before increasing the value.
For the Moré–Sorensen loop logger, the logger prints the following columns:
Iter: Moré–Sorensen iteration counter (within the current R2N step computation).σ: current primal regularization parameter of the augmented system.α: current dual regularization parameter of the augmented system.‖y‖: norm of the dual step computed by solving the augmented system, compared against the trust-region radiusΔ.Δ: current trust-region radius.inertia: observed inertia $(n_+, n_0, n_-)$ of the augmented system, i.e., the number of positive, zero, and negative eigenvalues.lsolve: status reported by the linear solver for the last system solved.descent: whether the computed step was found to be a descent direction for the quadratic model (true/false); seems_accept_descent.
For example,
using CUTEst, Penelopt
nlp = CUTEstModel("BT7")
stats = L2Penalty(nlp; print_level = 3)┌ Info:
│ This is Penelopt.jl v0.1.0.
│ Running with linear solver LDLFactorizations.jl v0.10.2.
│
│ Problem name: BT7
│ All variables: ████████████████████ 5 All constraints: ████████████████████ 3
│ free: ████████████████████ 5 free: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 lower: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 upper: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 low/upp: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ fixed: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 fixed: ████████████████████ 3
│ infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 infeas: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ nnzh: ( 60.00% sparsity) 6 linear: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ nonlinear: ████████████████████ 3
│ nnzj: ( 46.67% sparsity) 8
│ lin_nnzj: (------% sparsity)
│ nln_nnzj: ( 46.67% sparsity) 8
│
└
[ Info: ------------------------------------------------------------------------------------------------------
[ Info: Iter sIter Objective pfeas dfeas τ ptol dtol ‖x‖
[ Info: ------------------------------------------------------------------------------------------------------
[ Info: 0 0 +9.0900000e+02 3.44e+03 4.00e+00 1.03e+03 1.00e+00 1.00e+00 2.83e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.03e+03 ‖c(x)‖₂ with tolerance 1.00e+00...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +5.7728911e+03 Inf Inf 2.22e-16 +0.00e+00 2.83e+00 6.94e-310
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.22e+02 2.22e-16 4.07e+02 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 1 0 +4.6709605e+03 4.00e+00 1.37e+03 7.40e+01 +1.83e-01 2.87e+00 2.30e+00
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 7.40e+02 2.22e-16 1.39e+02 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 2 0 +2.9029691e+03 4.37e+00 7.70e+02 2.47e+02 +3.72e-01 2.30e+00 1.71e+00
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.47e+02 2.22e-16 5.88e+02 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 3 0 +1.7076691e+03 2.80e+00 3.82e+02 8.22e+01 +6.23e-01 1.46e+00 1.63e+00
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 8.22e+01 2.22e-16 5.41e+02 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 4 0 +1.3012830e+03 1.63e+00 5.80e+02 2.74e+01 +7.27e-01 7.69e-01 1.51e+00
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.74e+01 2.22e-16 1.88e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 5 0 +2.9219305e+03 1.07e+00 3.41e+02 9.14e+00 +3.64e-01 2.35e+00 2.32e+00
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 9.14e+03 2.22e-16 2.18e+04 1.03e+03 (5,0,3) success false
[ Info: | 1 9.14e+03 1.79e-04 1.51e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 6 1 +3.3219848e+02 2.64e+00 6.26e+03 3.05e+03 +1.01e+00 2.34e+00 5.64e-01
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 3.05e+03 2.22e-16 6.49e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 3.05e+03 1.41e-04 1.04e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 7 1 +2.7243130e+02 1.72e-01 3.79e+03 1.02e+03 +1.00e+00 2.36e+00 5.56e-02
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.02e+03 2.22e-16 3.23e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 1.02e+03 1.28e-04 1.04e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 8 1 +2.6756062e+02 1.37e-01 1.06e+02 3.38e+02 +1.00e+00 2.38e+00 5.99e-02
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 3.38e+02 2.22e-16 2.22e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 3.38e+02 1.17e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 9 1 +2.6538496e+02 1.21e-01 4.71e+01 1.13e+02 +1.00e+00 2.41e+00 5.82e-02
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.13e+02 2.22e-16 1.83e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 1.13e+02 1.10e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 10 1 +2.6494735e+02 1.10e-01 1.37e+01 3.76e+01 +1.00e+00 2.44e+00 3.64e-02
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 3.76e+01 2.22e-16 1.69e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 3.76e+01 1.07e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 11 1 +2.6492031e+02 1.04e-01 3.01e+00 1.25e+01 +1.00e+00 2.45e+00 1.13e-02
┌ Info: |
│ | Subproblem solved with status first_order after 11 iterations.
│ | Reached dfeas = 0.32948563926746943
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 1 11 +1.5087784e+02 1.02e-01 3.29e-01 1.03e+03 1.02e-03 3.29e-03 2.45e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.03e+03 ‖c(x)‖₂ with tolerance 3.29e-03...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +2.6492031e+02 0.00e+00 3.29e-01 1.25e+01 +0.00e+00 2.45e+00 1.13e-02
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.25e+01 2.22e-16 1.65e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 1.25e+01 1.07e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 1 1 +2.6492001e+02 1.02e-01 3.29e-01 4.18e+00 +1.00e+00 2.45e+00 1.36e-03
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.03e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 4.18e+00 2.22e-16 1.64e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 4.18e+00 1.07e-04 1.03e+03 1.03e+03 (5,0,3) success false
[ Info: | 2 4.18e+00 1.07e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 2 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 2 2 +2.6492001e+02 1.01e-01 1.30e-02 1.39e+00 +1.00e+00 2.45e+00 6.91e-06
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 2.078326150973622e-5
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 2 2 +1.5121076e+02 1.01e-01 2.08e-05 1.36e+03 1.02e-03 5.12e-05 2.67e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.36e+03 ‖c(x)‖₂ with tolerance 5.12e-05...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 2 +2.9459842e+02 0.00e+00 2.08e-05 1.39e+00 +0.00e+00 2.67e+00 6.91e-06
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.36e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.39e+00 2.22e-16 1.76e+03 1.36e+03 (5,0,3) success false
[ Info: | 1 1.39e+00 4.39e-05 1.36e+03 1.36e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 1 1 +2.9193260e+02 4.66e-02 1.03e+02 4.64e-01 +1.00e+00 2.66e+00 1.98e-02
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.36e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 4.64e-01 2.22e-16 1.79e+03 1.36e+03 (5,0,3) success false
[ Info: | 1 4.64e-01 4.34e-05 1.36e+03 1.36e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 2 1 +2.9193044e+02 5.49e-02 1.89e+00 1.55e-01 +1.00e+00 2.66e+00 3.58e-03
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 0.001227789363797617
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 3 2 +2.1212673e+02 5.43e-02 1.23e-03 1.78e+03 1.02e-03 5.12e-05 2.92e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.78e+03 ‖c(x)‖₂ with tolerance 5.12e-05...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +3.2390866e+02 0.00e+00 1.23e-03 1.55e-01 +0.00e+00 2.92e+00 3.58e-03
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.78e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.55e-01 2.22e-16 1.88e+03 1.78e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 1 0 +3.0658010e+02 1.16e-02 1.31e+02 5.16e-02 +1.00e+00 2.96e+00 4.20e-02
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.78e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 5.16e-02 2.22e-16 1.89e+03 1.78e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 2 0 +3.0650001e+02 5.82e-05 5.08e+00 1.72e-02 +1.00e+00 2.96e+00 1.54e-04
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 8.363531196664553e-5
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 4 2 +3.0650000e+02 3.26e-09 8.36e-05 1.78e+03 7.45e-08 5.12e-05 2.96e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.78e+03 ‖c(x)‖₂ with tolerance 5.12e-05...
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +3.0650001e+02 0.00e+00 8.36e-05 1.72e-02 +0.00e+00 2.96e+00 1.54e-04
┌ Info: | -----------------------------------------------------------------------------------------------------
│ | Computing step ( H + σI Jᵀ )(s) = -(∇f)
└ | ( J -αI )(y) = -(c ), with ‖y‖ ≤ 1.78e+03...
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.72e-02 2.22e-16 1.89e+03 1.78e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 1 0 +3.0650000e+02 3.26e-09 8.36e-05 5.73e-03 +1.00e+00 2.96e+00 7.70e-10
┌ Info: |
│ | Subproblem solved with status first_order after 1 iterations.
│ | Reached dfeas = 1.3229532817634647e-11
└ | ----------------------------------------------------------------------------------------------------------
[ Info: 5 1 +3.0650000e+02 3.89e-13 1.32e-11 1.78e+03 7.45e-08 5.12e-05 2.96e+00
┌ Info:
│ Number of Iterations: 5
│
│
│ Objective...........: +3.064999999992104e+02
│ Primal Feasibility..: 3.888001032237298e-13
│ Dual Feasibility....: 1.322953281763465e-11
│
│
└ EXIT: first_order.The lsolve column reports the status returned directly by the chosen linear_solver (see options) for the corresponding factorization/solve. A value other than success typically triggers either a regularization increase or a fallback strategy (e.g., switching MUMPS to an indefinite factorization), and does not necessarily indicate that the overall Moré–Sorensen iteration failed.