Dual convention

[odow]

What is Uno's dual convention? Currently, Uno returns the negative of the Ipopt dual:

See the

  Dual solution :
    c : 1.00000e+00

and

  Dual solution :
    c : -1.00000e+00

parts of the output.

Uno

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 >= 0)
           @objective(model, Min, -x)
           @constraint(model, c, x <= 2)
           optimize!(model)
           solution_summary(model; verbose = true)
       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, 1 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   │ -              │ -            │ -0.00999999 │ 0             │ 0.5          │ 1.99            │ initial point          │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 1     │ 1       │ 0.1            │ 1           │ OPT   │ 0              │ 0.10895      │ -0.11895    │ 0             │ 0.905001     │ 1.00152         │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 2     │ 1       │ 0.1            │ 1           │ OPT   │ 0              │ 1.86224      │ -1.98119    │ 0             │ 0.819074     │ 0.854585        │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 3     │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.000696375  │ -1.98049    │ 0             │ 2e-07        │ 0.0202932       │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 4     │ 1       │ 0.000150424    │ 1           │ OPT   │ 0              │ 0.0191597    │ -1.99965    │ 0             │ 2.47172e-05  │ 0.000347198     │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 5     │ 1       │ 1.84491e-06    │ 1           │ OPT   │ 0              │ 0.000345352  │ -2          │ 0             │ 1.84491e-11  │ 1.84513e-06     │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼───────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 6     │ 1       │ 2.5059e-09     │ 1           │ OPT   │ 0              │ 1.84262e-06  │ -2          │ 0             │ 2.52021e-14  │ 2.5076e-09      │ accepted (f-type)      │
└───────┴─────────┴────────────────┴─────────────┴───────┴────────────────┴──────────────┴─────────────┴───────────────┴──────────────┴─────────────────┴────────────────────────┘


Uno (LS feasibility_restoration waechter_filter_method primal_dual_interior_point)
Mon Oct 21 09:12:37 2024
────────────────────────────────────────
Status:					Converged with feasible KKT point
Objective value:			-2
Primal feasibility:			0
┌ Stationarity residual:		2.520206e-14
└ Complementarity residual:		2.507601e-09
┌ Feasibility stationarity residual:	2.520206e-14
└ Feasibility complementarity residual:	2.507601e-09
┌ Infeasibility measure:		0
│ Objective measure:			-2
└ Auxiliary measure:			4.788985e-08
CPU time:				0.002786s
Iterations:				6
Objective evaluations:			7
Constraints evaluations:		8
Objective gradient evaluations:		8
Jacobian evaluations:			8
Hessian evaluations:			6
Number of subproblems solved:		6
* Solver : AmplNLWriter

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

* Candidate solution (result #1)
  Primal status      : FEASIBLE_POINT
  Dual status        : FEASIBLE_POINT
  Objective value    : -2.00000e+00
  Dual objective value : -2.00000e+00
  Primal solution :
    x : 2.00000e+00
  Dual solution :
    c : 1.00000e+00

* Work counters
  Solve time (sec)   : 5.44970e-02

Ipopt

julia> begin
           model = Model() do
               return AmplNLWriter.Optimizer(Ipopt_jll.amplexe; directory = "/tmp/uno")
           end
           @variable(model, x >= 0)
           @objective(model, Min, -x)
           @constraint(model, c, x <= 2)
           optimize!(model)
           solution_summary(model; verbose = true)
       end
Ipopt 3.14.16: 

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

This is Ipopt version 3.14.16, running with linear solver MUMPS 5.7.3.

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        1
Number of nonzeros in Lagrangian Hessian.............:        0

Total number of variables............................:        1
                     variables with only lower bounds:        1
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        1
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        1

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0 -9.9999900e-03 0.00e+00 5.00e-01  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1 -1.1894999e-01 0.00e+00 9.05e-01  -1.0 1.09e-01    -  5.22e-01 1.00e+00f  1
   2 -1.9811895e+00 0.00e+00 4.24e-01  -1.7 3.15e+00    -  9.26e-02 5.91e-01f  1
   3 -1.9794257e+00 0.00e+00 2.00e-07  -1.7 1.76e-03    -  1.00e+00 1.00e+00f  1
   4 -1.9996449e+00 0.00e+00 2.86e-05  -3.8 2.02e-02    -  9.97e-01 1.00e+00f  1
   5 -1.9999982e+00 0.00e+00 1.84e-11  -5.7 3.53e-04    -  1.00e+00 1.00e+00f  1
   6 -2.0000000e+00 0.00e+00 2.51e-14  -8.6 1.84e-06    -  1.00e+00 1.00e+00f  1

Number of Iterations....: 6

                                   (scaled)                 (unscaled)
Objective...............:  -2.0000000174923991e+00   -2.0000000174923991e+00
Dual infeasibility......:   2.5148488989747521e-14    2.5148488989747521e-14
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   2.5076007968172859e-09    2.5076007968172859e-09
Overall NLP error.......:   2.5076007968172859e-09    2.5076007968172859e-09


Number of objective function evaluations             = 7
Number of objective gradient evaluations             = 7
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 7
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 7
Number of Lagrangian Hessian evaluations             = 6
Total seconds in IPOPT                               = 0.003

EXIT: Optimal Solution Found.
* Solver : AmplNLWriter

* Status
  Result count       : 1
  Termination status : LOCALLY_SOLVED
  Message from the solver:
  "Ipopt 3.14.16: Optimal Solution Found"

* Candidate solution (result #1)
  Primal status      : FEASIBLE_POINT
  Dual status        : FEASIBLE_POINT
  Objective value    : -2.00000e+00
  Dual objective value : -2.00000e+00
  Primal solution :
    x : 2.00000e+00
  Dual solution :
    c : -1.00000e+00

* Work counters
  Solve time (sec)   : 8.67858e-02

[cvanaret]

Uno and IPOPT/ASL (AMPL Solver Library) have a different Lagrangian definition:

• Uno: $\mathcal{L}(x, y, z) = f(x) - y^T c(x) - z$
• IPOPT: $\mathcal{L}(x, y, z) = f(x) + y^T c(x) - z$
• ASL: $\nabla^2 \mathcal{L}(x, y, z) = \nabla^2 f(x) + \sum_{j=1}^m y_j \nabla^2 c(x)$. Not sure about the bound duals in the Lagrangian.

For the Hessian evaluation, Uno's call to the ASL function lagscale_ASL with scaling factor -1 compensates for that.

Can you post the nl file? I can't reproduce at the moment since ASL transforms the constraint into a bound. Uno finds the following primal-dual solution:

Primal solution:			2 
┌ Constraint multipliers:		
│ Lower bound multipliers:		1.252103e-09 
└ Upper bound multipliers:		-1

so there has to be something wrong in the way Uno calls ASL's write_sol function.

[odow]

g3 1 1 0
 1 1 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 1 1
 0 0
 0 0 0 0 0
C0
n0
O0 0
n0
x1
0 0
r
1 2
b
2 0
k0
J0 1
0 1
G0 1
0 -1

[odow]

Different dual conventions are the bane of my life. Each time I hook up a new solver, I always encounter issues. I generally solve it by randomly whacking a bunch of - in places.

What do you do if the objective sense is Maximization?

[cvanaret]

If I maximize, I flip the sign of the objective (and its derivatives).
Here's Uno's primal-solution on your nl file. It has the right signs.

Primal solution:			2 2 
┌ Constraint multipliers:		-1 
│ Lower bound multipliers:		1.252103e-09 0 
└ Upper bound multipliers:		0 -1

So I think I should do another call to lagscale_ASL (with scaling factor 1) just before writing the solution.

[odow]

Here's the current model.sol

shell> cat /tmp/uno/model.sol

Options
3
1
1
0
1
1
1
1
1.000000001252078
2.000000017492399
objno 0 0

I think we're looking for

shell> cat /tmp/uno/model.sol

Options
3
1
1
0
1
1
1
1
-1.000000001252078
2.000000017492399
objno 0 0

[cvanaret]

Got it.
I tried another call to lagscale_ASL but it has no effect when the coefficient is 1 (it doesn't revert any existing change). I'll write on the AMPL forum.

[odow]

Did you try lagscale_ASL with another -1? (To flip the flip?)

[odow]

lagscale_ASL(asl, 1) is a no-op:
https://github.com/ampl/asl/blob/2f5d9de248c53a3063bba23af2013cd3db768bf8/src/solvers/conscale.c#L166-L167

[cvanaret]

@odow this should be fixed in commit fd9ad8f.

[odow]

So the dual now matches AMPL for minimization. But not for maximization.

We should also think about returning suffixes for the dual of the variable bounds.

julia> using JuMP, AmplNLWriter, Uno_jll, Ipopt_jll, Test

julia> function main(args...)
           @testset "main" begin
               @testset "Model 1" begin
                   model = Model(
                       () -> AmplNLWriter.Optimizer(args...; directory = "/tmp"),
                   )
                   @variable(model, x)
                   @objective(model, Min, x)
                   c1 = @constraint(model, x >= 1)
                   optimize!(model)
                   @test dual(c1) ≈ 1.0 atol=1e-6
                   @info "Model 1"
                   @info " model.nl"
                   print(read("/tmp/model.nl", String))
                   @info " model.sol"
                   print(read("/tmp/model.sol", String))
               end
               @testset "Model 2" begin
                   model = Model(
                       () -> AmplNLWriter.Optimizer(args...; directory = "/tmp"),
                   )
                   @variable(model, x)
                   @objective(model, Max, x)
                   c1 = @constraint(model, x <= 1)
                   optimize!(model)
                   @test dual(c1) ≈ -1.0 atol=1e-6
                   @info "Model 2"
                   @info " model.nl"
                   print(read("/tmp/model.nl", String))
                   @info " model.sol"
                   print(read("/tmp/model.sol", String))
               end
               @testset "Model 3" begin
                   model = Model(
                       () -> AmplNLWriter.Optimizer(args...; directory = "/tmp"),
                   )
                   @variable(model, x >= 1)
                   @objective(model, Min, x)
                   optimize!(model)
                   @test dual(LowerBoundRef(x)) ≈ 1.0 atol=1e-6
                   @info "Model 3"
                   @info " model.nl"
                   print(read("/tmp/model.nl", String))
                   @info " model.sol"
                   print(read("/tmp/model.sol", String))
               end
               @testset "Model 4" begin
                   model = Model(
                       () -> AmplNLWriter.Optimizer(args...; directory = "/tmp"),
                   )
                   @variable(model, x <= 1)
                   @objective(model, Max, x)
                   optimize!(model)
                   @test dual(UpperBoundRef(x)) ≈ -1.0 atol=1e-6
                   @info "Model 4"
                   @info " model.nl"
                   print(read("/tmp/model.nl", String))
                   @info " model.sol"
                   print(read("/tmp/model.sol", String))
               end
           end
           return
       end
main (generic function with 1 method)

julia> main(Ipopt_jll.amplexe, ["print_level=0", "sb=yes"])
Ipopt 3.14.16: print_level=0
sb=yes

[ Info: Model 1
[ Info:  model.nl
g3 1 1 0
 1 1 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 1 1
 0 0
 0 0 0 0 0
C0
n0
O0 0
n0
x1
0 0
r
2 1
b
3
k0
J0 1
0 1
G0 1
0 1
[ Info:  model.sol
 
Ipopt 3.14.16: Optimal Solution Found

Options
3
1
1
0
1
1
1
1
1
0.9999999925059035
objno 0 0
suffix 4 0 13 0 0
ipopt_zU_out
suffix 4 0 13 0 0
ipopt_zL_out
Ipopt 3.14.16: print_level=0
sb=yes

[ Info: Model 2
[ Info:  model.nl
g3 1 1 0
 1 1 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 1 1
 0 0
 0 0 0 0 0
C0
n0
O0 1
n0
x1
0 0
r
1 1
b
3
k0
J0 1
0 1
G0 1
0 1
[ Info:  model.sol
 
Ipopt 3.14.16: Optimal Solution Found

Options
3
1
1
0
1
1
1
1
1
1.0000000074940965
objno 0 0
suffix 4 0 13 0 0
ipopt_zU_out
suffix 4 0 13 0 0
ipopt_zL_out
Ipopt 3.14.16: print_level=0
sb=yes

[ Info: Model 3
[ Info:  model.nl
g3 1 1 0
 1 0 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 0 1
 0 0
 0 0 0 0 0
O0 0
n0
x1
0 0
b
2 1
G0 1
0 1
[ Info:  model.sol
 
Ipopt 3.14.16: Optimal Solution Found

Options
3
1
1
0
0
0
1
1
0.9999999925059035
objno 0 0
suffix 4 0 13 0 0
ipopt_zU_out
suffix 4 1 13 0 0
ipopt_zL_out
0 1.000000000000025
Ipopt 3.14.16: print_level=0
sb=yes

[ Info: Model 4
[ Info:  model.nl
g3 1 1 0
 1 0 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 0 1
 0 0
 0 0 0 0 0
O0 1
n0
x1
0 0
b
1 1
G0 1
0 1
[ Info:  model.sol
 
Ipopt 3.14.16: Optimal Solution Found

Options
3
1
1
0
0
0
1
1
1.0000000074940965
objno 0 0
suffix 4 1 13 0 0
ipopt_zU_out
0 1.000000000000025
suffix 4 0 13 0 0
ipopt_zL_out
Test Summary: | Pass  Total  Time
main          |    4      4  0.6s

julia> main(Uno_jll.amplexe, ["logger=SILENT"])
[ Info: Model 1
[ Info:  model.nl
g3 1 1 0
 1 1 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 1 1
 0 0
 0 0 0 0 0
C0
n0
O0 0
n0
x1
0 0
r
2 1
b
3
k0
J0 1
0 1
G0 1
0 1
[ Info:  model.sol
Uno 1.1.0: Converged with feasible KKT point

Options
3
1
1
0
1
1
1
1
1
0.9999999925059035
objno 0 0
Model 2: Test Failed at REPL[61]:26
  Expression: ≈(dual(c1), -1.0, atol = 1.0e-6)
   Evaluated: 1.0 ≈ -1.0 (atol=1.0e-6)

Stacktrace:
  [1] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:672 [inlined]
  [2] macro expansion
    @ ./REPL[61]:26 [inlined]
  [3] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
  [4] macro expansion
    @ ./REPL[61]:19 [inlined]
  [5] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
  [6] main(::Function, ::Vararg{Any})
    @ Main ./REPL[61]:3
  [7] top-level scope
    @ REPL[63]:1
  [8] eval
    @ ./boot.jl:385 [inlined]
  [9] eval_user_input(ast::Any, backend::REPL.REPLBackend, mod::Module)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:150
 [10] repl_backend_loop(backend::REPL.REPLBackend, get_module::Function)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:246
 [11] start_repl_backend(backend::REPL.REPLBackend, consumer::Any; get_module::Function)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:231
 [12] run_repl(repl::REPL.AbstractREPL, consumer::Any; backend_on_current_task::Bool, backend::Any)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:389
 [13] run_repl(repl::REPL.AbstractREPL, consumer::Any)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:375
 [14] (::Base.var"#1013#1015"{Bool, Bool, Bool})(REPL::Module)
    @ Base ./client.jl:432
 [15] #invokelatest#2
    @ ./essentials.jl:892 [inlined]
 [16] invokelatest
    @ ./essentials.jl:889 [inlined]
 [17] run_main_repl(interactive::Bool, quiet::Bool, banner::Bool, history_file::Bool, color_set::Bool)
    @ Base ./client.jl:416
 [18] exec_options(opts::Base.JLOptions)
    @ Base ./client.jl:333
 [19] _start()
    @ Base ./client.jl:552
[ Info: Model 2
[ Info:  model.nl
g3 1 1 0
 1 1 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 1 1
 0 0
 0 0 0 0 0
C0
n0
O0 1
n0
x1
0 0
r
1 1
b
3
k0
J0 1
0 1
G0 1
0 1
[ Info:  model.sol
Uno 1.1.0: Converged with feasible KKT point

Options
3
1
1
0
1
1
1
1
-1
1.0000000074940965
objno 0 0
Model 3: Test Failed at REPL[61]:40
  Expression: ≈(dual(LowerBoundRef(x)), 1.0, atol = 1.0e-6)
   Evaluated: 0.0 ≈ 1.0 (atol=1.0e-6)

Stacktrace:
  [1] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:672 [inlined]
  [2] macro expansion
    @ ./REPL[61]:40 [inlined]
  [3] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
  [4] macro expansion
    @ ./REPL[61]:34 [inlined]
  [5] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
  [6] main(::Function, ::Vararg{Any})
    @ Main ./REPL[61]:3
  [7] top-level scope
    @ REPL[63]:1
  [8] eval
    @ ./boot.jl:385 [inlined]
  [9] eval_user_input(ast::Any, backend::REPL.REPLBackend, mod::Module)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:150
 [10] repl_backend_loop(backend::REPL.REPLBackend, get_module::Function)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:246
 [11] start_repl_backend(backend::REPL.REPLBackend, consumer::Any; get_module::Function)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:231
 [12] run_repl(repl::REPL.AbstractREPL, consumer::Any; backend_on_current_task::Bool, backend::Any)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:389
 [13] run_repl(repl::REPL.AbstractREPL, consumer::Any)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:375
 [14] (::Base.var"#1013#1015"{Bool, Bool, Bool})(REPL::Module)
    @ Base ./client.jl:432
 [15] #invokelatest#2
    @ ./essentials.jl:892 [inlined]
 [16] invokelatest
    @ ./essentials.jl:889 [inlined]
 [17] run_main_repl(interactive::Bool, quiet::Bool, banner::Bool, history_file::Bool, color_set::Bool)
    @ Base ./client.jl:416
 [18] exec_options(opts::Base.JLOptions)
    @ Base ./client.jl:333
 [19] _start()
    @ Base ./client.jl:552
[ Info: Model 3
[ Info:  model.nl
g3 1 1 0
 1 0 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 0 1
 0 0
 0 0 0 0 0
O0 0
n0
x1
0 0
b
2 1
G0 1
0 1
[ Info:  model.sol
Uno 1.1.0: Converged with feasible KKT point

Options
3
1
1
0
0
0
1
1
0.9999999925059035
objno 0 0
Model 4: Test Failed at REPL[61]:54
  Expression: ≈(dual(UpperBoundRef(x)), -1.0, atol = 1.0e-6)
   Evaluated: -0.0 ≈ -1.0 (atol=1.0e-6)

Stacktrace:
  [1] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:672 [inlined]
  [2] macro expansion
    @ ./REPL[61]:54 [inlined]
  [3] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
  [4] macro expansion
    @ ./REPL[61]:48 [inlined]
  [5] macro expansion
    @ ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/Test/src/Test.jl:1577 [inlined]
  [6] main(::Function, ::Vararg{Any})
    @ Main ./REPL[61]:3
  [7] top-level scope
    @ REPL[63]:1
  [8] eval
    @ ./boot.jl:385 [inlined]
  [9] eval_user_input(ast::Any, backend::REPL.REPLBackend, mod::Module)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:150
 [10] repl_backend_loop(backend::REPL.REPLBackend, get_module::Function)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:246
 [11] start_repl_backend(backend::REPL.REPLBackend, consumer::Any; get_module::Function)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:231
 [12] run_repl(repl::REPL.AbstractREPL, consumer::Any; backend_on_current_task::Bool, backend::Any)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:389
 [13] run_repl(repl::REPL.AbstractREPL, consumer::Any)
    @ REPL ~/.julia/juliaup/julia-1.10.5+0.x64.apple.darwin14/share/julia/stdlib/v1.10/REPL/src/REPL.jl:375
 [14] (::Base.var"#1013#1015"{Bool, Bool, Bool})(REPL::Module)
    @ Base ./client.jl:432
 [15] #invokelatest#2
    @ ./essentials.jl:892 [inlined]
 [16] invokelatest
    @ ./essentials.jl:889 [inlined]
 [17] run_main_repl(interactive::Bool, quiet::Bool, banner::Bool, history_file::Bool, color_set::Bool)
    @ Base ./client.jl:416
 [18] exec_options(opts::Base.JLOptions)
    @ Base ./client.jl:333
 [19] _start()
    @ Base ./client.jl:552
[ Info: Model 4
[ Info:  model.nl
g3 1 1 0
 1 0 1 0 0 0
 0 1
 0 0
 0 0 0
 0 0 0 1
 0 0 0 0 0
 0 1
 0 0
 0 0 0 0 0
O0 1
n0
x1
0 0
b
1 1
G0 1
0 1
[ Info:  model.sol
Uno 1.1.0: Converged with feasible KKT point

Options
3
1
1
0
0
0
1
1
1.0000000074940965
objno 0 0
Test Summary: | Pass  Fail  Total  Time
main          |    1     3      4  0.3s
  Model 1     |    1            1  0.1s
  Model 2     |          1      1  0.1s
  Model 3     |          1      1  0.1s
  Model 4     |          1      1  0.1s
ERROR: Some tests did not pass: 1 passed, 3 failed, 0 errored, 0 broken.

[cvanaret]

The duals should now match IPOPT's for minimization and maximization (commit 117641e).
I will open a separate issue for the bound duals using suffixes (but I must admit I don't understand sh*t about that section of the documentation).

[odow]

Just confirming that I think we have this correct now:

jump-dev/MathOptInterface.jl#2567 (comment)

[cvanaret]

Great, thanks!