Infeasibility detection

[odow]

Is this expected behavior? Failed with suboptimal point seems like the wrong status to report.

julia> using JuMP, AmplNLWriter, Uno_jll

julia> begin
           model = Model() do
               return AmplNLWriter.Optimizer(Uno_jll.amplexe; directory = "/tmp/uno")
           end
           set_attribute(model, "preset", "ipopt")
           set_attribute(model, "linear_solver", "MUMPS")
           @variable(model, x)
           @variable(model, y)
           @constraint(model, y == exp(x))
           @constraint(model, x == y^2)
           optimize!(model)
           solution_summary(model)
       end
Model /tmp/uno/model.nl
Options:
- AMPL_write_solution_to_file = yes
- BQPD_kmax = 500
- BQPD_print_subproblem = no
- LP_solver = BQPD
- LS_backtracking_ratio = 0.5
- LS_min_step_length = 5e-7
- LS_scale_duals_with_step_length = yes
- QP_solver = BQPD
- TR_activity_tolerance = 1e-6
- TR_aggressive_decrease_factor = 4
- TR_decrease_factor = 2
- TR_increase_factor = 2
- TR_min_radius = 1e-7
- TR_radius = 10.
- TR_radius_reset_threshold = 1e-4
- armijo_decrease_fraction = 1e-8
- armijo_tolerance = 1e-9
- barrier_damping_factor = 1e-5
- barrier_default_multiplier = 1
- barrier_initial_parameter = 0.1
- barrier_k_epsilon = 10
- barrier_k_mu = 0.2
- barrier_k_sigma = 1e10
- barrier_push_variable_to_interior_k1 = 1e-2
- barrier_push_variable_to_interior_k2 = 1e-2
- barrier_regularization_exponent = 0.25
- barrier_small_direction_factor = 10.
- barrier_smax = 100
- barrier_tau_min = 0.99
- barrier_theta_mu = 1.5
- barrier_update_fraction = 10
- constraint_relaxation_strategy = feasibility_restoration
- convexify_QP = false
- dual_regularization_fraction = 1e-8
- enforce_linear_constraints = no
- filter_beta = 0.99999
- filter_capacity = 50
- filter_fact = 1e4
- filter_gamma = 1e-8
- filter_sufficient_infeasibility_decrease_factor = 0.9
- filter_switching_infeasibility_exponent = 1.1
- filter_type = standard
- filter_ubd = 1e4
- function_scaling_factor = 100
- function_scaling_threshold = 100
- funnel_beta = 0.9999
- funnel_fact = 1.5
- funnel_gamma = 0.001
- funnel_kappa = 0.5
- funnel_require_acceptance_wrt_current_iterate = no
- funnel_ubd = 1.0
- funnel_update_strategy = 1
- globalization_mechanism = LS
- globalization_strategy = waechter_filter_method
- hessian_model = exact
- l1_constraint_violation_coefficient = 1000.
- l1_relaxation_decrease_factor = 10.
- l1_relaxation_epsilon1 = 0.1
- l1_relaxation_epsilon2 = 0.1
- l1_relaxation_fixed_parameter = no
- l1_relaxation_initial_parameter = 1.
- l1_relaxation_residual_small_threshold = 1e-12
- l1_small_duals_threshold = 1e-10
- least_square_multiplier_max_norm = 1e3
- linear_solver = MUMPS
- logger = INFO
- loose_tolerance = 1e-6
- loose_tolerance_consecutive_iteration_threshold = 15
- max_iterations = 2000
- nonmonotone_filter_number_dominated_entries = 3
- primal_regularization_decrease_factor = 3.
- primal_regularization_fast_increase_factor = 100.
- primal_regularization_initial_factor = 1e-4
- primal_regularization_lb = 1e-20
- primal_regularization_slow_increase_factor = 8.
- print_solution = no
- progress_norm = L1
- protect_actual_reduction_against_roundoff = yes
- regularization_failure_threshold = 1e40
- regularization_increase_factor = 2
- regularization_initial_value = 1e-4
- residual_norm = INF
- residual_scaling_threshold = 100.
- scale_functions = yes
- scale_residuals = yes
- sparse_format = COO
- statistics_LS_step_length_column_order = 10
- statistics_SOC_column_order = 9
- statistics_TR_radius_column_order = 10
- statistics_barrier_parameter_column_order = 8
- statistics_complementarity_column_order = 105
- statistics_dual_feasibility_column_order = 102
- statistics_funnel_width_column_order = 25
- statistics_major_column_order = 1
- statistics_minor_column_order = 2
- statistics_objective_column_order = 100
- statistics_penalty_parameter_column_order = 5
- statistics_primal_feasibility_column_order = 101
- statistics_print_header_every_iterations = 15
- statistics_regularization_column_order = 21
- statistics_restoration_phase_column_order = 20
- statistics_stationarity_column_order = 104
- statistics_status_column_order = 200
- statistics_step_norm_column_order = 31
- subproblem = primal_dual_interior_point
- switch_to_optimality_requires_linearized_feasibility = no
- switching_delta = 1
- switching_infeasibility_exponent = 2
- threshold_unsuccessful_attempts = 8
- time_limit = inf
- tolerance = 1e-8
- unbounded_objective_threshold = -1e20
Problem /tmp/uno/model.nl_scaled_equalityconstrained_boundrelaxed
2 variables, 2 constraints

Options:
- AMPL_write_solution_to_file = yes
- LS_backtracking_ratio = 0.5
- LS_min_step_length = 5e-7
- LS_scale_duals_with_step_length = yes
- armijo_decrease_fraction = 1e-8
- armijo_tolerance = 1e-9
- barrier_damping_factor = 1e-5
- barrier_default_multiplier = 1
- barrier_initial_parameter = 0.1
- barrier_k_epsilon = 10
- barrier_k_mu = 0.2
- barrier_k_sigma = 1e10
- barrier_push_variable_to_interior_k1 = 1e-2
- barrier_push_variable_to_interior_k2 = 1e-2
- barrier_regularization_exponent = 0.25
- barrier_small_direction_factor = 10.
- barrier_tau_min = 0.99
- barrier_theta_mu = 1.5
- barrier_update_fraction = 10
- constraint_relaxation_strategy = feasibility_restoration
- dual_regularization_fraction = 1e-8
- filter_beta = 0.99999
- filter_capacity = 50
- filter_fact = 1e4
- filter_gamma = 1e-8
- filter_sufficient_infeasibility_decrease_factor = 0.9
- filter_type = standard
- filter_ubd = 1e4
- function_scaling_threshold = 100
- globalization_mechanism = LS
- globalization_strategy = waechter_filter_method
- l1_constraint_violation_coefficient = 1000.
- least_square_multiplier_max_norm = 1e3
- linear_solver = MUMPS
- logger = INFO
- loose_tolerance = 1e-6
- loose_tolerance_consecutive_iteration_threshold = 15
- max_iterations = 2000
- primal_regularization_decrease_factor = 3.
- primal_regularization_fast_increase_factor = 100.
- primal_regularization_initial_factor = 1e-4
- primal_regularization_lb = 1e-20
- primal_regularization_slow_increase_factor = 8.
- progress_norm = L1
- protect_actual_reduction_against_roundoff = yes
- regularization_failure_threshold = 1e40
- residual_norm = INF
- residual_scaling_threshold = 100.
- scale_functions = yes
- sparse_format = COO
- statistics_LS_step_length_column_order = 10
- statistics_barrier_parameter_column_order = 8
- statistics_complementarity_column_order = 105
- statistics_major_column_order = 1
- statistics_minor_column_order = 2
- statistics_objective_column_order = 100
- statistics_primal_feasibility_column_order = 101
- statistics_print_header_every_iterations = 15
- statistics_regularization_column_order = 21
- statistics_restoration_phase_column_order = 20
- statistics_stationarity_column_order = 104
- statistics_status_column_order = 200
- statistics_step_norm_column_order = 31
- subproblem = primal_dual_interior_point
- switch_to_optimality_requires_linearized_feasibility = no
- switching_delta = 1
- switching_infeasibility_exponent = 2
- threshold_unsuccessful_attempts = 8
- time_limit = inf
- tolerance = 1e-8
- unbounded_objective_threshold = -1e20
┌───────┬─────────┬────────────────┬─────────────┬───────┬────────────────┬──────────────┬─────────────┬───────────────┬──────────────┬─────────────────┬────────────────────────┐
│ iter  │ LS iter │ barrier param. │ step length │ phase │ regularization │ step norm    │ objective   │ primal feas.  │ stationarity │ complementarity │ status                 │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 0     │ -       │ -              │ -           │ OPT   │ -              │ -            │ 0           │ 1             │ 0            │ 0               │ initial point          │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 1     │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 1            │ 0           │ 1             │ -            │ -               │ rejected (h-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 2       │ -              │ 0.5         │ -     │ -              │ 0.5          │ 0           │ 0.75          │ 0            │ 0               │ accepted (h-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 2     │ -       │ 0.02           │ -           │ OPT   │ -              │ -            │ -           │ -             │ -            │ -               │ -                      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 2     │ 1       │ 0.5            │ 1           │ FEAS  │ 0              │ 0.0483041    │ 0           │ 0.753481      │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 2       │ -              │ 0.5         │ -     │ -              │ 0.0241521    │ 0           │ 0.750873      │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 3       │ -              │ 0.25        │ -     │ -              │ 0.012076     │ 0           │ 0.750218      │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 4       │ -              │ 0.125       │ -     │ -              │ 0.00603802   │ 0           │ 0.750055      │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 5       │ -              │ 0.0625      │ -     │ -              │ 0.00301901   │ 0           │ 0.750014      │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 6       │ -              │ 0.03125     │ -     │ -              │ 0.0015095    │ 0           │ 0.750003      │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 7       │ -              │ 0.015625    │ -     │ -              │ 0.000754752  │ 0           │ 0.750001      │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 8       │ -              │ 0.0078125   │ -     │ -              │ 0.000377376  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 9       │ -              │ 0.00390625  │ -     │ -              │ 0.000188688  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 10      │ -              │ 0.00195312  │ -     │ -              │ 9.4344e-05   │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 11      │ -              │ 0.000976562 │ -     │ -              │ 4.7172e-05   │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ iter  │ LS iter │ barrier param. │ step length │ phase │ regularization │ step norm    │ objective   │ primal feas.  │ stationarity │ complementarity │ status                 │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 12      │ -              │ 0.000488281 │ -     │ -              │ 2.3586e-05   │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 13      │ -              │ 0.000244141 │ -     │ -              │ 1.1793e-05   │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 14      │ -              │ 0.00012207  │ -     │ -              │ 5.8965e-06   │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 15      │ -              │ 6.10352e-05 │ -     │ -              │ 2.94825e-06  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 16      │ -              │ 3.05176e-05 │ -     │ -              │ 1.47413e-06  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 17      │ -              │ 1.52588e-05 │ -     │ -              │ 7.37063e-07  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 18      │ -              │ 7.62939e-06 │ -     │ -              │ 3.68531e-07  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 19      │ -              │ 3.8147e-06  │ -     │ -              │ 1.84266e-07  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 20      │ -              │ 1.90735e-06 │ -     │ -              │ 9.21328e-08  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 21      │ -              │ 9.53674e-07 │ -     │ -              │ 4.60664e-08  │ 0           │ 0.75          │ -            │ -               │ rejected (restoration) │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ -       │ -              │ -           │ -     │ -              │ -            │ -           │ -             │ -            │ -               │ LS failed              │
└───────┴─────────┴────────────────┴─────────────┴───────┴────────────────┴──────────────┴─────────────┴───────────────┴──────────────┴─────────────────┴────────────────────────┘


Uno (LS feasibility_restoration waechter_filter_method primal_dual_interior_point)
Mon Oct 21 08:57:38 2024
────────────────────────────────────────
Status:					Failed with suboptimal point
Objective value:			0
Primal feasibility:			0.5
┌ Stationarity residual:		0
└ Complementarity residual:		0
┌ Feasibility stationarity residual:	0
└ Feasibility complementarity residual:	0
┌ Infeasibility measure:		0.75
│ Objective measure:			0
└ Auxiliary measure:			0
CPU time:				0.006235s
Iterations:				2
Objective evaluations:			3
Constraints evaluations:		25
Objective gradient evaluations:		4
Jacobian evaluations:			4
Hessian evaluations:			3
Number of subproblems solved:		2
* Solver : AmplNLWriter

* Status
  Result count       : 1
  Termination status : OTHER_LIMIT
  Message from the solver:
  ""

* Candidate solution (result #1)
  Primal status      : UNKNOWN_RESULT_STATUS
  Dual status        : NO_SOLUTION
  Objective value    : 0.00000e+00
  Dual objective value : 0.00000e+00

* Work counters
  Solve time (sec)   : 6.65090e-02


julia> print(read("/tmp/uno/model.nl", String))
g3 1 1 0
 2 2 1 0 2 0
 2 1
 0 0
 2 0 0
 0 0 0 1
 0 0 0 0 0
 4 0
 0 0
 0 0 0 0 0
C0
o1
v1
o44
v0
C1
o2
n-1
o2
v1
v1
O0 0
n0
x2
0 0
1 0
r
4 0
4 0
b
3
3
k1
2
J0 2
0 0
1 0
J1 2
0 1
1 0

[cvanaret]

Infeasibility is indeed not detected. Here, the line search during feasibility restoration fails and it could be that the termination criteria of the feasibility problem are not tested. I will investigate further.