Uno

A modern, modular solver for nonlinearly constrained nonconvex optimization

Uno (Unifying Nonlinear Optimization) is a C++ library that unifies methods for solving nonlinearly constrained optimization problems of the form:

$$ \begin{align} \min_{x \in \mathbb{R}^n} & ~f(x) \\ \text{s.t.} & ~c_L \le c(x) \le c_U \\ & ~x_L \le x \le x_U \\ \end{align} $$

The theoretical abstract framework for unifying nonlinearly constrained nonconvex optimization was developed by Charlie Vanaret (Argonne National Laboratory & Zuse-Institut Berlin) and Sven Leyffer (Argonne National Laboratory). Uno was designed and implemented by Charlie Vanaret. It is released under the MIT license (see the license file).

The contributors are (in alphabetical order): Oscar Dowson @odow, David Kiessling @david0oo, Alexis Montoison @amontoison, Manuel Schaich @worc4021, Silvio Traversaro @traversaro.

Unifying nonlinearly constrained nonconvex optimization

We argue that most optimization methods can be broken down into four generic ingredients:

• a constraint relaxation strategy: a systematic way to relax the nonlinear constraints;
• a subproblem: a local model of the (possibly relaxed) problem at the current primal-dual iterate;
• a globalization strategy: an acceptance test of the trial iterate;
• a globalization mechanism: a recourse action upon rejection of the trial iterate.

Uno implements the following strategies:

Any strategy combination can be automatically generated without any programming effort from the user. Note that all combinations do not necessarily result in sensible algorithms, or even convergent approaches. For more details, check out our preprint or my presentation at the ICCOPT 2022 conference.

Uno implements presets, that is strategy combinations that correspond to existing solvers (as well as hyperparameter values found in their documentations):

• filtersqp mimics filterSQP (trust-region feasibility restoration filter SQP method);
• ipopt mimics IPOPT (line-search feasibility restoration filter barrier method);
• byrd mimics Byrd's S $\ell_1$ QP (line-search $\ell_1$ merit S $\ell_1$ QP method).

Latest results (September 26, 2024)

Some of Uno combinations that correspond to existing solvers (called presets, see below) have been tested against state-of-the-art solvers on 429 small problems of the CUTEst benchmark. The figure below is a performance profile of Uno and state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO and CONOPT; it shows how many problems are solved for a given budget of function evaluations (1 time, 2 times, 4 times, ..., $2^x$ times the number of objective evaluations of the best solver for each instance).

All log files can be found here.

How to cite Uno

In an article

We have submitted our paper to the Mathematical Programming Computation journal. The preprint is available on ResearchGate.

Until it is published, you can use the following bibtex entry:

@unpublished{VanaretLeyffer2024,
  author = {Vanaret, Charlie and Leyffer, Sven},
  title = {Unifying nonlinearly constrained nonconvex optimization},
  year = {2024},
  note = {Submitted to Mathematical Programming Computation}
}

On social media

To mention Uno on Twitter, use @UnoSolver.
To mention Uno on LinkedIn, use #unosolver.

Installation instructions

See the INSTALL file.

Solving a problem with Uno

Controlling Uno via options

Options can be set in three different ways (with decreasing precedence):

• passing an option file (option_file=file) that contains option value on each line;
• setting a preset that mimics an existing solver (preset=[filtersqp|ipopt|byrd]);
• setting individual options (see the default options).

Interfaces

AMPL/nl files

To solve an AMPL model in the .nl format, type in the build directory: ./uno_ampl model.nl -AMPL [option=value ...]
where [option=value ...] is a list of options separated by spaces.

A couple of CUTEst instances are available in the /examples directory.

Julia

Uno can be installed in Julia via Uno_jll.jl and used via AmplNLWriter.jl. An example can be found here.

Combining strategies on the fly

For an overview of the available strategies, type: ./uno_ampl --strategies:

• to pick a globalization mechanism, use the argument : globalization_mechanism=[LS|TR]
• to pick a constraint relaxation strategy, use the argument: constraint_relaxation_strategy=[feasibility_restoration|l1_relaxation]
• to pick a globalization strategy, use the argument: globalization_strategy=[l1_merit|fletcher_filter_method|waechter_filter_method|funnel_method]
• to pick a subproblem method, use the argument: subproblem=[QP|LP|primal_dual_interior_point]