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).

Silvio Traversaro and Alexis Montoison contributed to the CMakeLists.

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 1.0 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 1.0 implements three 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).

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.

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}
}

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

See the INSTALL file.

At the moment, Uno only reads models from .nl files. A couple of CUTEst instances are available in the /examples directory.

To solve an AMPL model, type in the build directory: ./uno_ampl path_to_file/file.nl

To use Uno with Julia/JuMP, a solution in the short term is to use the package AmplNLWriter.jl to dump JuMP models into .nl files.

To pick a globalization mechanism, use the argument (choose one of the possible options in brackets): -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_strategy|waechter_filter_strategy]
To pick a subproblem method, use the argument: -subproblem [QP|LP|primal_dual_interior_point]
The options can be combined in the same command line.

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

To pick a preset, use the argument: -preset [filtersqp|ipopt|byrd]