The Uno (Unifying Nonconvex Optimization) solver

Specific Domains Optimization (Mathematical)
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Uno v2.0.0 is out!
Already available in your favorite language: Uno_jll.

The major changes are:

  • a more powerful unification framework with ingredients such as Hessian model (exact, identity, zero), regularization strategy (primal, primal-dual, none) and inequality handling method (inequality constrained, interior-point).

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  • the null space active-set QP solver BQPD is now available as precompiled binaries and a binary package BQPD_jll :partying_face: This means we can now use the filtersqp preset (trust-region filter SQP method) within Uno_jll:
julia> using JuMP, AmplNLWriter, Uno_jll
julia> options = String["preset=filtersqp", "QP_solver=BQPD"];
julia> model = Model(() -> AmplNLWriter.Optimizer(Uno_jll.amplexe, options));
julia> @variable(model, x <= 0.5, start = -2);
julia> @variable(model, y, start = 1);
julia> @objective(model, Min, 100 * (y - x^2)^2 + (1 - x)^2);
julia> @constraint(model, x*y >= 1);
julia> @constraint(model, x + y^2 >= 0);
julia> optimize!(model)
Original model /tmp/jl_gTmcsU/model.nl
2 variables, 2 constraints (0 equality, 2 inequality)
Reformulated model /tmp/jl_gTmcsU/model.nl
2 variables, 2 constraints (0 equality, 2 inequality)

Used overwritten options:
- QP_solver = BQPD
- TR_min_radius = 1e-8
- TR_radius = 10
- constraint_relaxation_strategy = feasibility_restoration
- filter_type = standard
- globalization_mechanism = TR
- globalization_strategy = fletcher_filter_method
- hessian_model = exact
- inequality_handling_method = inequality_constrained
- l1_constraint_violation_coefficient = 1.
- loose_tolerance = 1e-6
- progress_norm = L1
- protect_actual_reduction_against_roundoff = no
- regularization_strategy = none
- residual_norm = L2
- switch_to_optimality_requires_linearized_feasibility = yes
- tolerance = 1e-6

─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
 iter   TR iter  TR radius    phase  step norm   objective   primal feas  stationarity  complementarity  status          
─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
 0      -        1.0000e+01   OPT    -           9.0900e+02  4.0000e+00   2.4797e+03    0.0000e+00       initial point   
 1      1        1.0000e+01   OPT    2.0000e+00  2.6000e+01  1.0000e+00   5.5713e+03    2.8887e+03       ✔ (h-type)      
 2      1        1.0000e+01   OPT    -           -           -            -             -                infeasible subproblem
 2      1        1.0000e+01   FEAS   7.5000e-01  2.5250e+01  1.1250e+00   -             -                ✘ (restoration) 
 -      2        3.7500e-01   FEAS   3.7500e-01  4.1504e-01  9.5312e-01   3.9528e-01    0.0000e+00       ✔ (restoration) 
 3      1        7.5000e-01   FEAS   7.5000e-01  3.9312e+01  5.6250e-01   5.0000e-01    0.0000e+00       ✔ (restoration) 
 4      1        1.5000e+00   FEAS   1.1250e+00  3.0650e+02  0.0000e+00   1.6654e+04    1.4508e+04       ✔ (restoration) 
 5      1        1.5000e+00   OPT    0.0000e+00  3.0650e+02  0.0000e+00   0.0000e+00    0.0000e+00       0 primal step   
─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
 iter   TR iter  TR radius    phase  step norm   objective   primal feas  stationarity  complementarity  status          
─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

Uno 2.0.0 (TR Fletcher-filter restoration inequality-constrained method with exact Hessian and no regularization)
Mon Jul  7 15:13:07 2025
────────────────────────────────────────
Optimization status:					Success
Iterate status:				    		Feasible KKT point
Objective value:			    		306.5
Primal feasibility:			    		0
┌ Stationarity residual:				0
└ Complementarity residual:				0
┌ Feasibility stationarity residual:	0
└ Feasibility complementarity residual:	0
┌ Infeasibility measure:				0
│ Objective measure:					306.5
└ Auxiliary measure:					0
CPU time:								0.015675s
Iterations:								5
Objective evaluations:					3
Constraints evaluations:				7
Objective gradient evaluations:			6
Jacobian evaluations:					6
Hessian evaluations:					6
Number of subproblems solved:			7

cc @cgeoga

A comprehensive description of the changes from v1.3.0 can be found here.

I’m actively working on the following features:

  • L-BFGS Hessian approximation;
  • SLP-EQP method;
  • a barrier method that better exploits the structure of the original problem;
  • an exponential barrier method, an alternative to IPOPT’s log barrier method;
  • Python bindings.

If you’re attending the ICCOPT 2025 conference in two weeks, don’t miss our session on Recent advances in open-source continuous solvers with talks about the HiGHS, acados and Uno solvers.

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