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JSOSolvers.jl documentation

JSOSolvers.jl is a collection of Julia optimization solvers for nonlinear, potentially nonconvex, continuous optimization problems that are unconstrained or bound-constrained:

\[\begin{aligned} \min\; & f(x) \\ \text{s.t.}\; & \ell \leq x \leq u \end{aligned}\]

where $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a continuously differentiable function, with $\ell \in \left(\mathbb{R} \cup \{-\infty\} \right)^n$, and $u \in \left(\mathbb{R} \cup \{+\infty\} \right)^n$. The algorithms implemented here are iterative methods that aim to compute a stationary point of \eqref{eq:nlp} using first and, if possible, second-order derivatives.

This package provides optimization solvers curated by the JuliaSmoothOptimizers organization. Solvers in JSOSolvers.jl take as input an AbstractNLPModel, JSO's general model API defined in NLPModels.jl, a flexible data type to evaluate objective and constraints, their derivatives, and to provide any information that a solver might request from a model.

The solvers in JSOSolvers.jl adopt a matrix-free approach, where standard optimization methods are implemented without forming derivative matrices explicitly. This strategy enables the solution of large-scale problems even when function and gradient evaluations are expensive. The motivation is to solve large-scale unconstrained and bound-constrained problems such as parameter estimation in inverse problems, design optimization in engineering, and regularized machine learning models, and use these solvers to solve subproblems of penalty algorithms.

Installation

JSOSolvers is a registered package. To install this package, open the Julia REPL (i.e., execute the julia binary), type ] to enter package mode, and install JSOSolvers as follows

pkg> add JSOSolvers

Bug reports and discussions

If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.

If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.

Basic usage

All solvers here are JSO-Compliant, in the sense that they accept NLPModels and return GenericExecutionStats. This allows benchmark them easily.

All solvers can be called like the following:

stats = solver_name(nlp; kwargs...)

where nlp is an AbstractNLPModel or some specialization, such as an AbstractNLSModel, and the following keyword arguments are supported:

  • x is the starting default (default: nlp.meta.x0);
  • atol is the absolute stopping tolerance (default: atol = √ϵ);
  • rtol is the relative stopping tolerance (default: rtol = √ϵ);
  • max_eval is the maximum number of objective and constraints function evaluations (default: -1, which means no limit);
  • max_time is the maximum allowed elapsed time (default: 30.0);
  • stats is a SolverTools.GenericExecutionStats with the output of the solver.

See the full list of Solvers.