# The Uno (Unifying Nonlinear Optimization) solver
**URL:** https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883
**Category:** Optimization (Mathematical)
**Tags:** nonlinear-optimizati, nonconvex-optimizati, nonlinear-programmin, sqp
**Created:** [June 19, 2024, 8:23pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883 "2024-06-19T20:23:45Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [June 19, 2024, 8:23pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/1 "2024-06-19T20:23:45Z")
Dear all,
For the past 6 years, I have been working (on and off, this year full time) on **Uno** , a modular C++ solver for nonconvex optimization. It unifies the workflows of most gradient-based iterative methods (such as SQP and barrier methods) and allows the automatic combination of off-the-shelf strategies for step computation, globalization and constraint relaxation. It mimics existing solvers such as IPOPT, filterSQP and SNOPT, but also generates thoroughly novel optimization methods.
I have just published the [preprint](https://www.researchgate.net/publication/381522383) _Unifying nonlinearly constrained nonconvex optimization_ cowritten with [Sven Leyffer](https://www.anl.gov/profile/sven-leyffer) (Argonne National Laboratory).
The code is available on [Github](https://github.com/cvanaret/Uno) as open-source software under the MIT license.
At the moment, Uno only reads models from .nl files (AMPL). Interfaces to CasADi and Matlab are being independently developed and Iβm confident more interfaces will be available soon. Until a Julia/JuMP interface is available, you can dump your JuMP model into an .nl file with the [AmplNLWriter.jl](https://juliahub.com/ui/Packages/General/AmplNLWriter) library.
Future developments include L-BFGS Hessian approximation, funnel method (with [David Kiessling](https://www.mech.kuleuven.be/en/pma/research/meco/people/00140695)), trust-region barrier method, SLP-EQP method, parameterizable numerical type (double, float, quad precision and so on) and extension to broader classes of problems (problems with complementarity constraints, robust optimization).
Give Uno a try and give us some feedback π
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [June 20, 2024, 10:56pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/2 "2024-06-20T22:56:25Z")
I guess we should make a [Yggdrasil](https://github.com/JuliaPackaging/Yggdrasil) build so that we can install it automatically.
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [July 17, 2024, 6:21pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/3 "2024-07-17T18:21:42Z")
Donβt miss us at [ISMP](https://ismp2024.gerad.ca/) next week!
Sven will give the keynote presentation [Unifying nonlinearly constrained optimization](https://ismp2024.gerad.ca/schedule/T2/968) on July 23 (Tuesday) at 3pm. I will give the talk [Uno, a next-gen solver for unifying nonlinearly constrained nonconvex optimization](https://ismp2024.gerad.ca/schedule/FA/260) on July 26 (Friday) at 9am.
See you then π
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [September 26, 2024, 3:52pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/4 "2024-09-26T15:52:44Z")
Uno 1.1.0 is out! It now features:
- an interface to the open-source linear solver MUMPS.
- a new globalization strategy (a strategy that accepts or rejects trial iterates) called funnel method. According to [our tests](https://www.researchgate.net/publication/383660361), it performs at least better than filter methods (IPOPT, filterSQP), while easier to implement.
> **[GitHub - cvanaret/Uno: A next-gen solver for optimization with nonconvex...](https://github.com/cvanaret/Uno)**
>
> A next-gen solver for optimization with nonconvex objective and constraints. Unifies barrier and SQP methods in a modern and generic way, and unlocks a variety of novel methods. Competitive against filterSQP, IPOPT, SNOPT, MINOS and CONOPT.
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [October 13, 2024, 9:56am UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/5 "2024-10-13T09:56:01Z")
This solver could potentially be useful for Model Predictive Control (MPC), is this something you or any of your colleagues have tried? Do you have any feeling for what kind of overhead the AmplNLWriter interface adds? I have a feeling this would be prohibitive for using UNO for MPC from julia?
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [October 13, 2024, 1:12pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/6 "2024-10-13T13:12:19Z")
I havenβt, but Unoβs main beta tester [David Kiessling](https://www.mech.kuleuven.be/en/pma/research/meco/people/00140695) is writing his PhD on MPC. Weβve discussed future Uno developments that would benefit MPC, in particular quasi-Newton Hessian approximations and exploiting the structure of the problem. Iβm interested to see how Uno will hold up compared to state-of-the-art solvers!
At the moment, AmplNLWriter is just the easy way between Julia and Uno, but itβs probably not the most efficient way indeed. Ideally, Iβd need a JuMP interface. To be developed π
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [October 13, 2024, 1:24pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/7 "2024-10-13T13:24:58Z")
Here are the latest numerical results (Sept 26, 2024) of Uno against filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO and CONOPT on 429 small [CUTEst](https://arnold-neumaier.at/glopt/coconut/Benchmark/Library2_new_v1.html) test problems. It is a [Dolan-MorΓ© performance profile](https://link.springer.com/article/10.1007/s101070100263) (the higher and the more to the left, the better).
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 13, 2024, 7:19pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/8 "2024-10-13T19:19:37Z")
I think the blocker for writing a Julia interface was being able to compile it. Did we make any progress since [[Uno] add initial build\_tarballs.jl by odow Β· Pull Request #8937 Β· JuliaPackaging/Yggdrasil Β· GitHub](https://github.com/JuliaPackaging/Yggdrasil/pull/8937#issuecomment-2190139283)?
---
### Author:  [@metab0t](https://discourse.julialang.org/u/metab0t)
#### Post date: [October 14, 2024, 3:20am UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/9 "2024-10-14T03:20:37Z")
Is there any plan to provide IPOPT-like C API for Uno? I think it is the prerequisite for a Julia Interface and I plan to support it in PyOptInterface, too.
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [October 14, 2024, 12:39pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/10 "2024-10-14T12:39:32Z")
Yes, Iβll work on that at some point. It might be helpful for other interfaces as well.
---
### Author:  [@metab0t](https://discourse.julialang.org/u/metab0t)
#### Post date: [October 14, 2024, 2:58pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/11 "2024-10-14T14:58:49Z")
Will more LP/QP solvers like HiGHS, Gurobi, COPT be supported in the future? I see that you have prepared abstractions to support multiple LP/QP solvers in the codebase.
I am also curious about the decision to use BQPD as the primary LP/QP solver. Does it have special advantages compared with other solvers?
---
### Author:  [@amontoison](https://discourse.julialang.org/u/amontoison)
#### Post date: [October 14, 2024, 6:47pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/12 "2024-10-14T18:47:19Z")
Charlie, do you think that we could be allowed to cross-compile `BQPD` and get a `BQPD_jll.jl` with Yggdrasil so that we can use it in `Uno_jll.jl`?
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [October 14, 2024, 10:11pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/13 "2024-10-14T22:11:43Z")
Yes, the abstractions are here, only time is missing π I plan to interface at least HiGHS in the near future.
We started with BQPD because originally, Uno was meant to be a modern version of filterSQP (which uses BQPD). It is a nonconvex QP solver (it accommodates indefinite Hessians) and is matrix-free (it requires only Hessian-vector products, even though in practice we do form the explicit Hessian).
@amontoison thatβs a good idea. Let me ask Sven when we meet on Thursday.
Unoβs development is a one-person endeavor, so my to-do list tends to grow faster than it shrinks. If you know someone who would be willing to invest a bit of time and energy into Uno, please have them reach out π
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [October 28, 2024, 6:24am UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/14 "2024-10-28T06:24:43Z")
Just to update this thread:
Uno can now be installed automatically via Uno\_jll.jl, and used via AmplNLWriter.jl.
Hereβs an example:
```julia
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
βββββββββ¬ββββββββββ¬βββββββββββββββββ¬ββββββββββββββ¬ββββββββ¬βββββββββββββββββ¬βββββββββββββββ¬ββββββββββββββ¬βββββββββββββββ¬ββββββββββββββββββ¬βββββββββββββββββββββββββ
β iter β LS iter β barrier param. β step length β phase β regularization β step norm β objective β stationarity β complementarity β status β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 0 β - β - β - β OPT β - β - β 1 β 2 β 0 β initial point β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 1 β 1 β 0.1 β 1 β OPT β 0 β 1 β 100 β - β - β rejected (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β - β 2 β - β 0.5 β - β - β 0.5 β 6.5 β - β - β rejected (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β - β 3 β - β 0.25 β - β - β 0.25 β 0.953125 β 12.5 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 2 β 1 β 0.1 β 1 β OPT β 0 β 0.0902778 β 0.483206 β 1.01166 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 3 β 1 β 0.1 β 1 β OPT β 0 β 0.429389 β 3.46968 β - β - β rejected (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β - β 2 β - β 0.5 β - β - β 0.214695 β 0.457088 β 9.5274 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 4 β 1 β 0.1 β 1 β OPT β 0 β 0.0950542 β 0.188942 β 0.415353 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 5 β 1 β 0.02 β 1 β OPT β 0 β 0.349223 β 0.901785 β - β - β rejected (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β - β 2 β - β 0.5 β - β - β 0.174612 β 0.139187 β 6.5051 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 6 β 1 β 0.02 β 1 β OPT β 0 β 0.092873 β 0.054941 β 0.451043 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 7 β 1 β 0.02 β 1 β OPT β 0 β 0.248802 β 0.0720927 β - β - β rejected (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β - β 2 β - β 0.5 β - β - β 0.124401 β 0.0291446 β 2.26614 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 8 β 1 β 0.02 β 1 β OPT β 0 β 0.11047 β 0.00985865 β 1.15467 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 9 β 1 β 0.02 β 1 β OPT β 0 β 0.100021 β 0.00232375 β 1.00373 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β iter β LS iter β barrier param. β step length β phase β regularization β step norm β objective β stationarity β complementarity β status β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 10 β 1 β 0.02 β 1 β OPT β 0 β 0.0509267 β 0.000237972 β 0.218984 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 11 β 1 β 0.02 β 1 β OPT β 0 β 0.0253247 β 4.92674e-06 β 0.0595169 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 12 β 1 β 0.00282843 β 1 β OPT β 0 β 0.00319684 β 2.81895e-09 β 0.000831455 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 13 β 1 β 1.84491e-06 β 1 β OPT β 0 β 9.78057e-05 β 8.88178e-16 β 8.67623e-07 β 0 β accepted (f-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 14 β 1 β 2.5059e-09 β 1 β OPT β 0 β 4.65423e-08 β 0 β 2.46136e-13 β 0 β accepted (f-type) β
βββββββββ΄ββββββββββ΄βββββββββββββββββ΄ββββββββββββββ΄ββββββββ΄βββββββββββββββββ΄βββββββββββββββ΄ββββββββββββββ΄βββββββββββββββ΄ββββββββββββββββββ΄βββββββββββββββββββββββββ
Uno 1.1.0 (LS feasibility_restoration waechter_filter_method primal_dual_interior_point)
Mon Oct 28 19:21:41 2024
ββββββββββββββββββββββββββββββββββββββββ
Status: Converged with feasible KKT point
Objective value: 0
Primal feasibility: 0
β Stationarity residual: 2.461364e-13
β Complementarity residual: 0
β Feasibility stationarity residual: 2.461364e-13
β Feasibility complementarity residual: 0
β Infeasibility measure: 0
β Objective measure: 0
β Auxiliary measure: 0
Primal solution: 1 1
β Constraint multipliers:
β Lower bound multipliers: 0 0
β Upper bound multipliers: 0 0
β Constraint feasibility multipliers:
β Lower bound feasibility multipliers: 0 0
β 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
```
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [October 31, 2024, 1:55pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/15 "2024-10-31T13:55:52Z")
Iβm really grateful to @odow and @amontoison for their time (and their patience)!
Note that at the moment, the `ipopt` preset (whose strategy combination mimics IPOPT) is the only available preset in Uno\_jll.jl (it invokes the linear solver MUMPS\_jll.jl).
If you add constraints to Oscarβs model, you get my favorite problem [hs015.mod](https://vanderbei.princeton.edu/ampl/nlmodels/hs/hs015.mod):
```julia
julia> using AmplNLWriter, JuMP, Uno_jll
julia> model = Model(() -> AmplNLWriter.Optimizer(Uno_jll.amplexe));
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_cyAI59/model.nl
2 variables, 2 constraints
Reformulated model /tmp/jl_cyAI59/model.nl_scaled_equalityconstrained_boundrelaxed
4 variables, 2 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
βββββββββ¬ββββββββββ¬βββββββββββββββββ¬ββββββββββββββ¬ββββββββ¬βββββββββββββββββ¬βββββββββββββββ¬ββββββββββββββ¬ββββββββββββββββ¬βββββββββββββββ¬ββββββββββββββββββ¬βββββββββββββββββββββββββ
β iter β LS iter β barrier param. β step length β phase β regularization β step norm β objective β primal feas. β stationarity β complementarity β status β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌββββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 0 β - β - β - β OPT β - β - β 37.7805 β 4.02 β 39.2084 β 2.5 β initial point β
β 1 β 1 β 0.1 β 1 β OPT β 0 β 0.0233907 β 35.6959 β 3.955 β 107.546 β 1.52938 β accepted (h-type) β
β 2 β 1 β 0.1 β 1 β OPT β 0 β 1.98766 β 1.04159 β 1.24585 β 178.176 β 0.262071 β accepted (h-type) β
β 3 β 1 β 0.1 β 1 β OPT β 0 β 0.553065 β 0.40318 β 1.53048 β 185.734 β 0.107792 β accepted (h-type) β
β 4 β 1 β 0.1 β 1 β OPT β 10000 β 0.00125483 β 0.39945 β 1.52798 β 179.337 β 0.0780677 β accepted (h-type) β
β 5 β 1 β 0.1 β 1 β OPT β 0 β 2.07556 β 15.8289 β 4.80884 β - β - β rejected (filter) β
β - β 2 β - β 0.5 β - β - β 1.03778 β 2.9258 β 1.9662 β - β - β rejected (filter) β
β - β 3 β - β 0.25 β - β - β 0.518889 β 0.314168 β 1.44654 β 369.218 β 0.120012 β accepted (h-type) β
β 6 β 1 β 0.1 β 1 β OPT β 3333.33 β 0.00264217 β 0.314141 β 1.44304 β 362.915 β 0.0110483 β accepted (h-type) β
β 7 β 1 β 0.1 β 1 β OPT β 1111.11 β 0.000795601 β 0.314547 β 1.44252 β 363.966 β 0.0110967 β accepted (h-type) β
β 8 β 1 β 0.1 β 1 β OPT β 2962.96 β 0.18222 β 0.339671 β 1.33278 β 20376.9 β 15.7265 β accepted (h-type) β
β 9 β 1 β 0.1 β 1 β OPT β 0 β 0.00395733 β 0.342921 β 1.33029 β 18813.5 β 14.5924 β accepted (h-type) β
β 10 β 1 β 0.1 β 1 β OPT β 0 β 2.16096 β 12.7717 β 2.15844 β - β - β rejected (filter) β
β - β 2 β - β 0.5 β - β - β 1.08048 β 4.31384 β 1.20475 β 16589.6 β 12.6198 β accepted (h-type) β
β 11 β 1 β 0.1 β 1 β OPT β 0 β 0.630084 β 5.8819 β 0.952354 β 1007.7 β 0.463586 β accepted (h-type) β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌββββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β iter β LS iter β barrier param. β step length β phase β regularization β step norm β objective β primal feas. β stationarity β complementarity β status β
βββββββββΌββββββββββΌβββββββββββββββββΌββββββββββββββΌββββββββΌβββββββββββββββββΌβββββββββββββββΌββββββββββββββΌββββββββββββββββΌβββββββββββββββΌββββββββββββββββββΌβββββββββββββββββββββββββ€
β 12 β 1 β 0.1 β 1 β OPT β 0 β 2.28896 β 12.7534 β 0.316297 β 969.044 β 0.206543 β accepted (h-type) β
β 13 β 1 β 0.1 β 1 β OPT β 0 β 0.318652 β 12.763 β 4.01388e-07 β 0.237094 β 0.107368 β accepted (h-type) β
β 14 β 1 β 0.02 β 1 β OPT β 0 β 0.00351111 β 12.779 β 1.01312e-06 β 0.000127402 β 0.0200148 β accepted (f-type) β
β 15 β 1 β 0.000150424 β 1 β OPT β 0 β 0.00955038 β 12.7393 β 6.68257e-06 β 5.06342e-05 β 0.000192227 β accepted (f-type) β
β 16 β 1 β 1.84491e-06 β 1 β OPT β 0 β 7.29582e-05 β 12.739 β 4.68065e-10 β 3.49192e-09 β 1.848e-06 β accepted (f-type) β
β 17 β 1 β 2.5059e-09 β 1 β OPT β 0 β 8.86474e-07 β 12.739 β 5.82867e-14 β 4.13891e-13 β 2.50627e-09 β accepted (f-type) β
βββββββββ΄ββββββββββ΄βββββββββββββββββ΄ββββββββββββββ΄ββββββββ΄βββββββββββββββββ΄βββββββββββββββ΄ββββββββββββββ΄ββββββββββββββββ΄βββββββββββββββ΄ββββββββββββββββββ΄βββββββββββββββββββββββββ
Uno 1.1.0 (LS feasibility_restoration waechter_filter_method primal_dual_interior_point)
Thu Oct 31 14:46:55 2024
ββββββββββββββββββββββββββββββββββββββββ
Status: Converged with feasible KKT point
Objective value: 306.5
Primal feasibility: 5.240253e-14
β Stationarity residual: 4.138911e-13
β Complementarity residual: 2.506267e-09
β Feasibility stationarity residual: 4.138911e-13
β Feasibility complementarity residual: 2.506267e-09
β Infeasibility measure: 5.828671e-14
β Objective measure: 12.73898
β Auxiliary measure: 1.146775e-07
Primal solution: 0.5 2 1 4.5
β Constraint multipliers: 700 1.339957e-08
β Lower bound multipliers: 0 0 29.09393 5.569483e-10
β Upper bound multipliers: -1751 0 0 0
β Constraint feasibility multipliers: 0 0
β Lower bound feasibility multipliers: 0 0 0 0
β Upper bound feasibility multipliers: 0 0 0 0
Objective multiplier: 1
CPU time: 0.00495s
Iterations: 17
Objective evaluations: 21
Constraints evaluations: 22
Objective gradient evaluations: 19
Jacobian evaluations: 19
Hessian evaluations: 17
Number of subproblems solved: 17
```
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [November 18, 2024, 9:18am UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/16 "2024-11-18T09:18:12Z")
[Uno 1.3.0](https://github.com/cvanaret/Uno/releases/tag/v1.3.0) now features:
- an interface to the LP solver HiGHS, available via the option `LP_solver=HiGHS` (QP coming soon!);
- a new preset `filterslp` (a trust-region restoration filter Sequential Linear Programming), available via the option `preset=filterslp`.
Hereβs the same example (hs015.mod) as in the previous message solved with the `filterslp` preset:
```julia
using JuMP, AmplNLWriter, Uno_jll
function Optimizer()
# pass options here
options = String["preset=filterslp", "LP_solver=HiGHS"]
return AmplNLWriter.Optimizer(Uno_jll.amplexe, options)
end
model = Model(() -> Optimizer());
@variable(model, x <= 0.5, start = -2);
@variable(model, y, start = 1);
@objective(model, Min, 100 * (y - x^2)^2 + (1 - x)^2);
@constraint(model, x*y >= 1);
@constraint(model, x + y^2 >= 0);
optimize!(model)
```
```shell
Original model /tmp/jl_EMUrZq/model.nl
2 variables, 2 constraints
Reformulated model /tmp/jl_EMUrZq/model.nl
2 variables, 2 constraints
Used overwritten options:
- LP_solver = HiGHS
- TR_min_radius = 1e-8
- TR_radius = 10
- constraint_relaxation_strategy = feasibility_restoration
- filter_type = standard
- globalization_mechanism = TR
- globalization_strategy = fletcher_filter_method
- l1_constraint_violation_coefficient = 1.
- loose_tolerance = 1e-4
- progress_norm = L1
- protect_actual_reduction_against_roundoff = no
- residual_norm = L2
- sparse_format = CSC
- subproblem = LP
- switch_to_optimality_requires_linearized_feasibility = yes
- tolerance = 1e-5
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
iter TR iter TR radius phase step norm objective primal feas stationarity complementarity status
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
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 2.5000e+00 2.5250e+01 6.2500e-01 2.3805e+03 1.8750e+02 β (f-type)
2 1 1.0000e+01 OPT 1.2500e+00 3.0650e+02 0.0000e+00 5.5902e+02 0.0000e+00 β (h-type)
3 1 1.0000e+01 OPT 0.0000e+00 3.0650e+02 0.0000e+00 0.0000e+00 0.0000e+00 0 primal step
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
Uno 1.3.0 (TR feasibility_restoration fletcher_filter_method LP)
Mon Nov 18 10:12:16 2024
ββββββββββββββββββββββββββββββββββββββββ
Status: Converged with feasible KKT point
Objective value: 306.5
Primal feasibility: 0
β Stationarity residual: 0
β Complementarity residual: 0
β Feasibility stationarity residual: 0
β Feasibility complementarity residual: 0
β Infeasibility measure: 0
β Objective measure: 306.5
β Auxiliary measure: 0
CPU time: 0.003727s
Iterations: 3
Objective evaluations: 4
Constraints evaluations: 4
Objective gradient evaluations: 4
Jacobian evaluations: 4
Hessian evaluations: 0
Number of subproblems solved: 3
```
---
### Author:  [@cgeoga](https://discourse.julialang.org/u/cgeoga)
#### Post date: [November 18, 2024, 9:24pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/17 "2024-11-18T21:24:07Z")
This is really interesting. Iβve been watching `Uno` for a long time because the problems I work on (Gaussian process MLE computation) really seem to benefit from the trust region paradigm, and an open-source library that mimics `filtersqp` seems like a really great new tool.
How distant is the feature of direct access to `Uno` in the sense of not needing to go through AMPL? I have always assumed that AMPL really was for settings where people could write their problem pretty simply in closed form like the `hs*` examples. But my code applications often look like this:
```julia
using StaticArrays, LinearAlgebra, BesselK, JuMP, AmplNLWriter, Uno_jll, Ipopt, ForwardDiff
Optimizer() = AmplNLWriter.Optimizer(Uno_jll.amplexe, String["preset=ipopt"])
# Generate some fake data to fit a GP model to.
const pts = rand(SVector{2,Float64}, 100)
const sim = let K = [matern(x, y, (1.0, 0.1, 0.75)) for x in pts, y in pts]
L = cholesky(Symmetric(K)).L
L*randn(length(pts))
end
# negative log-likelihood for GP data with three-parameter Matern model.
function _nll(pv)
K = [matern(x, y, pv) for x in pts, y in pts]
Kf = cholesky!(Symmetric(K))
(logdet(Kf) + sum(abs2, Kf.U'\sim))/2
end
# If the optimizer steps somewhere infeasible or just takes the range param. to a huge
# number, the Cholesky will fail. So this try-catch is necessary to avoid a hard
# crash that the optimizer doesn't recover from.
nll(p...) = (try; return _nll(p); catch; return NaN; end)
# MLE computation:
function mle()
model = Model(Ipopt.Optimizer) # Model(()->Optimizer())
@variable(model, 0.0 <= scale, start=1.0)
@variable(model, 0.0 <= range, start=0.01)
@variable(model, 0.25 <= smoothness <= 5.0, start=1.0)
@operator(model, op_nll, 3, nll)
@objective(model, Min, op_nll(scale, range, smoothness))
optimize!(model)
JuMP.is_solved_and_feasible(model) || throw(error("Optimization failed!"))
value.([scale, range, smoothness])
end
```
As you can see I did out of curiosity try the AMPL interface, but predictably this setting where my objective function sort of requires carrying around a ton of information doesnβt work. I have no idea how much additional work it is to allow users to access the solver by providing objective/constraint, objective grad/constraint jacobian, and Lagrangian Hessian (like `Ipopt` and Iβm sure many others). But as soon as that is possible, I will probably migrate a lot of workflows over!
Also, off-topic, but this `@operator` syntax is pretty nice! Thanks @odow.
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [November 18, 2024, 9:42pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/18 "2024-11-18T21:42:12Z")
> How distant is the feature of direct access to `Uno` in the sense of not needing to go through AMPL?
I assume, distant. It requires someone to write a C API a la Ipopt.
Using `@operator` with `AmplNLWriter` is not on the roadmap. In theory it is possible, but it requires being able to compile a C shared library on the userβs machine. Perhaps we could revisit once static compilation with Julia is trivial.
Finally, note that you cannot use `filtersqp` through Uno\_jll because we cannot distribute the non-free BQPD, which Uno uses to solve QPs.
---
### Author:  [@cgeoga](https://discourse.julialang.org/u/cgeoga)
#### Post date: [November 18, 2024, 10:10pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/19 "2024-11-18T22:10:19Z")
Oof. Brutal, brutal, and brutal. Iβd still love to find a way to use this somehow, but I suppose Iβll have to stay patient. Just dreaming of the day I stop paying for KNITROβ¦
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [November 19, 2024, 12:27pm UTC](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883/20 "2024-11-19T12:27:39Z")
Thanks @cgeoga! As @odow said, weβll need a proper C API. Itβs of course on my to-do list (like many other things π
).
Good news: we started discussions about extending the HiGHS QP solver to indefinite quadratic optimization. This would be a great open-source alternative to BQPD and we could finally run the `filtersqp` preset in Uno the way it was meant to be.
[Next page](https://discourse.julialang.org/t/the-uno-unifying-nonlinear-optimization-solver/115883.md?page=2)