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 v1.0.0.
│ Running with linear solver MUMPS v5.8.2.
│
│ ScaledModel{Float64, Vector{Float64}, CUTEst.CUTEstModel{Float64}, NLPModels.NLPModelMeta{Float64, Vector{Float64}}}
│ Problem name: BT7 (scaled)
│ 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
│
│ Counters:
│ obj: ████████████████████ 1 grad: ████████████████████ 1 cons: ████████████████████ 1
│ cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jac: ████████████████████ 1 jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 hess: ████████████████████ 1 hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
└
[ 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 17 +1.5160191e+02 1.01e-01 4.16e-01 1.03e+03 1.01e-03 4.16e-03 2.45e+00
[ Info: 2 1 +1.5123102e+02 1.01e-01 2.22e-03 1.36e+03 1.01e-03 5.12e-05 2.67e+00
[ Info: 3 2 +2.1215012e+02 5.43e-02 8.67e-04 1.78e+03 1.01e-03 5.12e-05 2.92e+00
[ Info: 4 2 +3.0650000e+02 3.24e-09 8.29e-05 1.78e+03 7.45e-08 5.12e-05 2.96e+00
[ Info: 5 1 +3.0650000e+02 3.89e-13 9.75e-12 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....: 9.748977013519171e-12
│
│
└ 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.- An iteration type symbol:
w(active watchdog),↗(step rejected,σincreased),=(step accepted,σunchanged),↘(step accepted,σdecreased). ‖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 v1.0.0.
│ Running with linear solver MUMPS v5.8.2.
│
│ ScaledModel{Float64, Vector{Float64}, CUTEst.CUTEstModel{Float64}, NLPModels.NLPModelMeta{Float64, Vector{Float64}}}
│ Problem name: BT7 (scaled)
│ 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
│
│ Counters:
│ obj: ████████████████████ 1 grad: ████████████████████ 1 cons: ████████████████████ 1
│ cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jac: ████████████████████ 1 jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 hess: ████████████████████ 1 hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
└
[ 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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +5.7728911e+03 Inf Inf 4.93e-32 +0.00e+00 2.83e+00 5.22e-310
[ Info: | 1 0 +2.7548283e+03 4.00e+00 1.37e+03 1.64e+02 +4.97e-01 ↘ 2.25e+00 1.93e+00
[ Info: | 2 1 +1.6755576e+03 2.34e+00 8.49e+02 5.48e+02 +6.65e-01 ↘ 1.63e+00 8.28e-01
[ Info: | 3 1 +1.1175802e+03 1.49e+00 1.07e+03 1.83e+02 +8.86e-01 ↘ 1.02e+00 7.88e-01
[ Info: | 4 0 +1.1175802e+03 1.03e+00 5.47e+02 5.48e+02 -3.22e+00 ↗ 1.02e+00 3.32e+00
[ Info: | 5 1 +1.2304267e+03 1.03e+00 2.62e+03 1.83e+02 +1.01e+00 ↘ 1.05e+00 7.81e-01
[ Info: | 6 1 +1.0813191e+03 9.24e-01 6.73e+02 6.09e+02 +9.86e-01 ↘ 8.67e-01 2.20e-01
[ Info: | 7 1 +1.0602701e+03 9.41e-01 3.75e+02 2.03e+03 +9.99e-01 ↘ 8.27e-01 5.50e-02
[ Info: | 8 1 +1.0361019e+03 9.41e-01 3.17e+02 6.76e+02 +9.97e-01 ↘ 7.61e-01 9.20e-02
[ Info: | 9 1 +1.0212129e+03 9.41e-01 1.75e+02 2.25e+02 +9.98e-01 ↘ 6.97e-01 1.26e-01
[ Info: | 10 0 +1.0212129e+03 9.43e-01 5.79e+01 6.76e+02 -1.46e+02 ↗ 6.97e-01 1.99e+01
[ Info: | 11 1 +9.5915751e+02 9.43e-01 6.83e+03 2.25e+02 +1.02e+00 ↘ 8.74e-01 4.78e-01
[ Info: | 12 0 +9.5915751e+02 9.22e-01 3.09e+02 6.76e+02 -1.41e+00 ↗ 8.74e-01 3.77e+00
[ Info: | 13 1 +1.1083953e+03 9.22e-01 1.17e+03 2.25e+02 +5.03e-01 ↘ 2.35e+00 1.79e+00
[ Info: | 14 0 +3.8487991e+02 8.30e-01 8.08e+02 7.51e+01 +6.53e-01 ↘ 2.20e+00 7.88e-01
[ Info: | 15 0 +2.8505855e+02 1.89e-01 1.17e+03 2.50e+01 +9.24e-01 ↘ 2.71e+00 5.95e-01
[ Info: | 16 1 +2.6680194e+02 5.17e-02 2.03e+02 8.35e+00 +9.92e-01 ↘ 2.51e+00 2.23e-01
[ Info: | 17 1 +2.6492480e+02 8.51e-02 4.96e+01 2.78e+00 +9.98e-01 ↘ 2.45e+00 6.57e-02
┌ Info: |
│ | Subproblem solved with status first_order after 17 iterations.
│ | Reached dfeas = 0.41555139041326594
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 1 17 +1.5160191e+02 1.01e-01 4.16e-01 1.03e+03 1.01e-03 4.16e-03 2.45e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.03e+03 ‖c(x)‖₂ with tolerance 4.16e-03...
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +2.6492480e+02 0.00e+00 4.16e-01 2.78e+00 +0.00e+00 2.45e+00 6.57e-02
[ Info: | 1 1 +2.6492001e+02 1.01e-01 4.16e-01 9.28e-01 +1.00e+00 ↘ 2.45e+00 1.14e-03
┌ Info: |
│ | Subproblem solved with status first_order after 1 iterations.
│ | Reached dfeas = 0.0022228983464348514
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 2 1 +1.5123102e+02 1.01e-01 2.22e-03 1.36e+03 1.01e-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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +2.9460719e+02 0.00e+00 2.22e-03 9.28e-01 +0.00e+00 2.67e+00 1.14e-03
[ Info: | 1 1 +2.9193993e+02 4.66e-02 1.03e+02 3.09e-01 +1.00e+00 ↘ 2.66e+00 1.98e-02
[ Info: | 2 1 +2.9193772e+02 5.49e-02 1.89e+00 1.03e-01 +1.00e+00 ↘ 2.66e+00 3.62e-03
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 0.0008665757225116977
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 3 2 +2.1215012e+02 5.43e-02 8.67e-04 1.78e+03 1.01e-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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +3.2392967e+02 0.00e+00 8.67e-04 1.03e-01 +0.00e+00 2.92e+00 3.62e-03
[ Info: | 1 0 +3.0657999e+02 1.16e-02 1.31e+02 3.44e-02 +1.00e+00 ↘ 2.96e+00 4.19e-02
[ Info: | 2 0 +3.0650001e+02 5.77e-05 5.07e+00 1.15e-02 +1.00e+00 ↘ 2.96e+00 1.53e-04
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 8.285143394459737e-5
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 4 2 +3.0650000e+02 3.24e-09 8.29e-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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +3.0650001e+02 0.00e+00 8.29e-05 1.15e-02 +0.00e+00 2.96e+00 1.53e-04
[ Info: | 1 0 +3.0650000e+02 3.24e-09 8.29e-05 3.82e-03 +1.00e+00 ↘ 2.96e+00 7.63e-10
┌ Info: |
│ | Subproblem solved with status first_order after 1 iterations.
│ | Reached dfeas = 9.748977013519171e-12
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 5 1 +3.0650000e+02 3.89e-13 9.75e-12 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....: 9.748977013519171e-12
│
│
└ 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 v1.0.0.
│ Running with linear solver MUMPS v5.8.2.
│
│ ScaledModel{Float64, Vector{Float64}, CUTEst.CUTEstModel{Float64}, NLPModels.NLPModelMeta{Float64, Vector{Float64}}}
│ Problem name: BT7 (scaled)
│ 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
│
│ Counters:
│ obj: ████████████████████ 1 grad: ████████████████████ 1 cons: ████████████████████ 1
│ cons_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 cons_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jcon: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jgrad: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jac: ████████████████████ 1 jac_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jac_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jtprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jtprod_lin: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jtprod_nln: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 hess: ████████████████████ 1 hprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
│ jhess: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0 jhprod: ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 0
└
[ 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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +5.7728911e+03 Inf Inf 4.93e-32 +0.00e+00 2.83e+00 9.80e-310
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 4.93e+02 2.22e-16 3.35e+02 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 1 0 +2.7548283e+03 4.00e+00 1.37e+03 1.64e+02 +4.97e-01 ↘ 2.25e+00 1.93e+00
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.64e+03 2.22e-16 2.90e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 1.64e+03 1.17e-03 1.08e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 2 1 +1.6755576e+03 2.34e+00 8.49e+02 5.48e+02 +6.65e-01 ↘ 1.63e+00 8.28e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 5.48e+02 2.22e-16 2.48e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 5.48e+02 8.79e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 3 1 +1.1175802e+03 1.49e+00 1.07e+03 1.83e+02 +8.86e-01 ↘ 1.02e+00 7.88e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.83e+02 2.22e-16 3.62e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 4 0 +1.1175802e+03 1.03e+00 5.47e+02 5.48e+02 -3.22e+00 ↗ 1.02e+00 3.32e+00
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 5.48e+02 2.22e-16 3.50e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 5.48e+02 8.37e-04 1.44e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 5 1 +1.2304267e+03 1.03e+00 2.62e+03 1.83e+02 +1.01e+00 ↘ 1.05e+00 7.81e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.83e+03 2.22e-16 1.49e+04 1.03e+03 (5,0,3) success false
[ Info: | 1 1.83e+03 9.72e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 6 1 +1.0813191e+03 9.24e-01 6.73e+02 6.09e+02 +9.86e-01 ↘ 8.67e-01 2.20e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 6.09e+03 2.22e-16 1.06e+05 1.03e+03 (5,0,3) success false
[ Info: | 1 6.09e+03 9.72e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 7 1 +1.0602701e+03 9.41e-01 3.75e+02 2.03e+03 +9.99e-01 ↘ 8.27e-01 5.50e-02
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.03e+03 2.22e-16 7.55e+04 1.03e+03 (5,0,3) success false
[ Info: | 1 2.03e+03 9.57e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 8 1 +1.0361019e+03 9.41e-01 3.17e+02 6.76e+02 +9.97e-01 ↘ 7.61e-01 9.20e-02
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 6.76e+02 2.22e-16 1.44e+05 1.03e+03 (5,0,3) success false
[ Info: | 1 6.76e+02 9.50e-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 +1.0212129e+03 9.41e-01 1.75e+02 2.25e+02 +9.98e-01 ↘ 6.97e-01 1.26e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.25e+02 2.22e-16 1.37e+05 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 10 0 +1.0212129e+03 9.43e-01 5.79e+01 6.76e+02 -1.46e+02 ↗ 6.97e-01 1.99e+01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 6.76e+02 2.22e-16 4.03e+04 1.03e+03 (5,0,3) success false
[ Info: | 1 6.76e+02 9.29e-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 +9.5915751e+02 9.43e-01 6.83e+03 2.25e+02 +1.02e+00 ↘ 8.74e-01 4.78e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.25e+02 2.22e-16 4.57e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 12 0 +9.5915751e+02 9.22e-01 3.09e+02 6.76e+02 -1.41e+00 ↗ 8.74e-01 3.77e+00
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 6.76e+02 2.22e-16 2.55e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 6.76e+02 4.94e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 13 1 +1.1083953e+03 9.22e-01 1.17e+03 2.25e+02 +5.03e-01 ↘ 2.35e+00 1.79e+00
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.25e+02 2.22e-16 2.17e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 14 0 +3.8487991e+02 8.30e-01 8.08e+02 7.51e+01 +6.53e-01 ↘ 2.20e+00 7.88e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 7.51e+01 2.22e-16 1.73e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 0 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 15 0 +2.8505855e+02 1.89e-01 1.17e+03 2.50e+01 +9.24e-01 ↘ 2.71e+00 5.95e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.50e+01 2.22e-16 1.85e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 2.50e+01 8.86e-05 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 16 1 +2.6680194e+02 5.17e-02 2.03e+02 8.35e+00 +9.92e-01 ↘ 2.51e+00 2.23e-01
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 8.35e+00 2.22e-16 1.67e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 8.35e+00 1.06e-04 1.03e+03 1.03e+03 (5,0,3) success true
┌ Info: |
│ | Step computed with status first_order after 1 iterations.
└ | -----------------------------------------------------------------------------------------------------
[ Info: | 17 1 +2.6492480e+02 8.51e-02 4.96e+01 2.78e+00 +9.98e-01 ↘ 2.45e+00 6.57e-02
┌ Info: |
│ | Subproblem solved with status first_order after 17 iterations.
│ | Reached dfeas = 0.41555139041326594
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 1 17 +1.5160191e+02 1.01e-01 4.16e-01 1.03e+03 1.01e-03 4.16e-03 2.45e+00
┌ Info: | ----------------------------------------------------------------------------------------------------------------
└ | Solving subproblem minₓ f(x) + 1.03e+03 ‖c(x)‖₂ with tolerance 4.16e-03...
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | Iter sIter Objective pfeas dfeas σ ρ Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +2.6492480e+02 0.00e+00 4.16e-01 2.78e+00 +0.00e+00 2.45e+00 6.57e-02
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 2.78e+00 2.22e-16 1.63e+03 1.03e+03 (5,0,3) success false
[ Info: | 1 2.78e+00 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 1.01e-01 4.16e-01 9.28e-01 +1.00e+00 ↘ 2.45e+00 1.14e-03
┌ Info: |
│ | Subproblem solved with status first_order after 1 iterations.
│ | Reached dfeas = 0.0022228983464348514
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 2 1 +1.5123102e+02 1.01e-01 2.22e-03 1.36e+03 1.01e-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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +2.9460719e+02 0.00e+00 2.22e-03 9.28e-01 +0.00e+00 2.67e+00 1.14e-03
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 9.28e-01 2.22e-16 1.76e+03 1.36e+03 (5,0,3) success false
[ Info: | 1 9.28e-01 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 +2.9193993e+02 4.66e-02 1.03e+02 3.09e-01 +1.00e+00 ↘ 2.66e+00 1.98e-02
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 3.09e-01 2.22e-16 1.79e+03 1.36e+03 (5,0,3) success false
[ Info: | 1 3.09e-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 +2.9193772e+02 5.49e-02 1.89e+00 1.03e-01 +1.00e+00 ↘ 2.66e+00 3.62e-03
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 0.0008665757225116977
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 3 2 +2.1215012e+02 5.43e-02 8.67e-04 1.78e+03 1.01e-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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 1 +3.2392967e+02 0.00e+00 8.67e-04 1.03e-01 +0.00e+00 2.92e+00 3.62e-03
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.03e-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 +3.0657999e+02 1.16e-02 1.31e+02 3.44e-02 +1.00e+00 ↘ 2.96e+00 4.19e-02
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 3.44e-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 5.77e-05 5.07e+00 1.15e-02 +1.00e+00 ↘ 2.96e+00 1.53e-04
┌ Info: |
│ | Subproblem solved with status first_order after 2 iterations.
│ | Reached dfeas = 8.285143394459737e-5
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 4 2 +3.0650000e+02 3.24e-09 8.29e-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 Type ‖x‖ ‖s‖
[ Info: | ----------------------------------------------------------------------------------------------------------------
[ Info: | 0 0 +3.0650001e+02 0.00e+00 8.29e-05 1.15e-02 +0.00e+00 2.96e+00 1.53e-04
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | Iter σ α ‖y‖ Δ inertia lsolve descent
[ Info: | -----------------------------------------------------------------------------------------------------
[ Info: | 0 1.15e-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 3.24e-09 8.29e-05 3.82e-03 +1.00e+00 ↘ 2.96e+00 7.63e-10
┌ Info: |
│ | Subproblem solved with status first_order after 1 iterations.
│ | Reached dfeas = 9.748977013519171e-12
└ | ----------------------------------------------------------------------------------------------------------------
[ Info: 5 1 +3.0650000e+02 3.89e-13 9.75e-12 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....: 9.748977013519171e-12
│
│
└ 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.