Add optimisation solver: Uno

[jbcaillau]

https://github.com/cvanaret/Uno
(still needs a Julia interface)

to be discussed with @cvanaret

[cvanaret]

Hi there,
Thanks to the patient guidance of Oscar Dowson and Alexis Montoison, Uno can now be installed in Julia via Uno_jll.jl and used via AmplNLWriter.jl:

julia> using AmplNLWriter, JuMP, Uno_jll

julia> model = Model(() -> AmplNLWriter.Optimizer(Uno_jll.amplexe));

julia> @variable(model, x);

julia> @variable(model, y);

julia> @objective(model, Min, (1 - x)^2 + 100 * (y - x^2)^2);

julia> optimize!(model)
Original model /var/folders/bg/dzq_hhvx1dxgy6gb5510pxj80000gn/T/jl_bVsNQH/model.nl
2 variables, 0 constraints
Reformulated model /var/folders/bg/dzq_hhvx1dxgy6gb5510pxj80000gn/T/jl_bVsNQH/model.nl_scaled_equalityconstrained_boundrelaxed
2 variables, 0 constraints

Used overwritten options:
- LS_backtracking_ratio = 0.5
- LS_min_step_length = 5e-7
- LS_scale_duals_with_step_length = yes
- armijo_decrease_fraction = 1e-8
- barrier_damping_factor = 1e-5
- barrier_tau_min = 0.99
- constraint_relaxation_strategy = feasibility_restoration
- filter_beta = 0.99999
- filter_fact = 1e4
- filter_gamma = 1e-8
- filter_type = standard
- filter_ubd = 1e4
- globalization_mechanism = LS
- globalization_strategy = waechter_filter_method
- l1_constraint_violation_coefficient = 1000.
- linear_solver = MUMPS
- loose_tolerance = 1e-6
- loose_tolerance_consecutive_iteration_threshold = 15
- progress_norm = L1
- protect_actual_reduction_against_roundoff = yes
- residual_norm = INF
- scale_functions = yes
- sparse_format = COO
- subproblem = primal_dual_interior_point
- switch_to_optimality_requires_linearized_feasibility = no
- switching_delta = 1
- tolerance = 1e-8

┌───────┬─────────┬────────────────┬─────────────┬───────┬────────────────┬──────────────┬─────────────┬──────────────┬─────────────────┬────────────────────────┐
│ iter  │ LS iter │ barrier param. │ step length │ phase │ regularization │ step norm    │ objective   │ stationarity │ complementarity │ status                 │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 0     │ -       │ -              │ -           │ OPT   │ -              │ -            │ 1           │ 2            │ 0               │ initial point          │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 1     │ 1       │ 0.1            │ 1           │ OPT   │ 0              │ 1            │ 100         │ -            │ -               │ rejected (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 2       │ -              │ 0.5         │ -     │ -              │ 0.5          │ 6.5         │ -            │ -               │ rejected (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 3       │ -              │ 0.25        │ -     │ -              │ 0.25         │ 0.953125    │ 12.5         │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 2     │ 1       │ 0.1            │ 1           │ OPT   │ 0              │ 0.0902778    │ 0.483206    │ 1.01166      │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 3     │ 1       │ 0.1            │ 1           │ OPT   │ 0              │ 0.429389     │ 3.46968     │ -            │ -               │ rejected (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 2       │ -              │ 0.5         │ -     │ -              │ 0.214695     │ 0.457088    │ 9.5274       │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 4     │ 1       │ 0.1            │ 1           │ OPT   │ 0              │ 0.0950542    │ 0.188942    │ 0.415353     │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 5     │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.349223     │ 0.901785    │ -            │ -               │ rejected (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 2       │ -              │ 0.5         │ -     │ -              │ 0.174612     │ 0.139187    │ 6.5051       │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 6     │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.092873     │ 0.054941    │ 0.451043     │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 7     │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.248802     │ 0.0720927   │ -            │ -               │ rejected (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ -     │ 2       │ -              │ 0.5         │ -     │ -              │ 0.124401     │ 0.0291446   │ 2.26614      │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 8     │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.11047      │ 0.00985865  │ 1.15467      │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 9     │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.100021     │ 0.00232375  │ 1.00373      │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ iter  │ LS iter │ barrier param. │ step length │ phase │ regularization │ step norm    │ objective   │ stationarity │ complementarity │ status                 │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 10    │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.0509267    │ 0.000237972 │ 0.218984     │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 11    │ 1       │ 0.02           │ 1           │ OPT   │ 0              │ 0.0253247    │ 4.92674e-06 │ 0.0595169    │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 12    │ 1       │ 0.00282843     │ 1           │ OPT   │ 0              │ 0.00319684   │ 2.81895e-09 │ 0.000831455  │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 13    │ 1       │ 1.84491e-06    │ 1           │ OPT   │ 0              │ 9.78057e-05  │ 8.88178e-16 │ 8.67623e-07  │ 0               │ accepted (f-type)      │
├───────┼─────────┼────────────────┼─────────────┼───────┼────────────────┼──────────────┼─────────────┼──────────────┼─────────────────┼────────────────────────┤
│ 14    │ 1       │ 2.5059e-09     │ 1           │ OPT   │ 0              │ 4.65423e-08  │ 0           │ 2.46136e-13  │ 0               │ accepted (f-type)      │
└───────┴─────────┴────────────────┴─────────────┴───────┴────────────────┴──────────────┴─────────────┴──────────────┴─────────────────┴────────────────────────┘

Uno 1.1.0 (LS feasibility_restoration waechter_filter_method primal_dual_interior_point)
Mon Oct 28 19:21:41 2024
────────────────────────────────────────
Status:					Converged with feasible KKT point
Objective value:			0
Primal feasibility:			0
┌ Stationarity residual:		2.461364e-13
└ Complementarity residual:		0
┌ Feasibility stationarity residual:	2.461364e-13
└ Feasibility complementarity residual:	0
┌ Infeasibility measure:		0
│ Objective measure:			0
└ Auxiliary measure:			0
Primal solution:			1 1 
┌ Constraint multipliers:		
│ Lower bound multipliers:		0 0 
└ Upper bound multipliers:		0 0 
┌ Constraint feasibility multipliers:	
│ Lower bound feasibility multipliers:	0 0 
└ Upper bound feasibility multipliers:	0 0 
Objective multiplier:			1
CPU time:				0.00863s
Iterations:				14
Objective evaluations:			20
Constraints evaluations:		0
Objective gradient evaluations:		16
Jacobian evaluations:			0
Hessian evaluations:			14
Number of subproblems solved:		14

julia> solution_summary(model)
* Solver : AmplNLWriter

* Status
  Result count       : 1
  Termination status : LOCALLY_SOLVED
  Message from the solver:
  "Uno 1.1.0: Converged with feasible KKT point"

* Candidate solution (result #1)
  Primal status      : FEASIBLE_POINT
  Dual status        : NO_SOLUTION
  Objective value    : 4.43734e-29
  Dual objective value : 4.43734e-29

* Work counters
  Solve time (sec)   : 3.24550e-01

I'll be in touch when we have a proper Julia interface ;)

[jbcaillau]

hi @cvanaret ; sorry for the late feedback and thanks for the update. we'll be glad to add uno as soon as you think it makes sense (e.g. trough a reasonable Julia API) 🤞🏾

[jbcaillau]

hi @cvanaret uno is in our pipe, check

should allow nice benchmarks, see e.g. https://github.com/orgs/control-toolbox/discussions/69#discussioncomment-14750567

guidelines welcome!

[cvanaret]

Cool, looking forward!

You can start from the examples given here. Basically, Uno gives you SQP methods or interior-point methods, and I've picked sets of hyperparameters/options that mimic state-of-the-art solvers filterSQP and IPOPT.
All you have to do is pass the value filtersqp or ipopt to the preset keyword, as can be seen in the examples 🙂

[PierreMartinon]

@ocots @jbcaillau This should be moved to CTSolvers ;-)