SLEQP

Introduction

SLEQP is a software package for large-scale nonlinear optimization. It is designed to find (local) solutions of mathematical optimization problems of the form

``` min f(x) x ∈ ℝⁿ

s.t. l ≤ c(x) ≤ u xl ≤ x ≤ xu ```

where f: ℝⁿ --> ℝ is the optimization objective, and c: ℝⁿ --> ℝᵐ are optimization constraints.

The vectors l, u ∈ ℝᵐ denote the lower and upper bounds on the nonlinear constraints, while the vectors x_l, x_u ∈ ℝⁿ are bounds on the variables. The functions f(x) and c(x) can be nonlinear and nonconvex, but should be twice continuously differentiable.

Publication

Details regarding this implementation may be found in the accompanying article

Hansknecht, C., & Kirches, C. (2023). SLEQP: An open-source package for nonlinear programming. Proceedings in Applied Mathematics and Mechanics, 00, e202300241. https://doi.org/10.1002/pamm.202300241

Dependencies

For the solution of the linear programming problem, one of the following linear programming libraries is required:

• Gurobi
• HiGHS
• SoPlex

For factorizations, one of the following factorization libraries is required:

• CHOLMOD
• Umfpack
• MUMPS
• MA27
• MA57
• MA86
• MA97
• SPQR

Additional dependencies: * trlib for nonconvex trust region QP solving

Optional dependencies for the python bindings: * Python itself, including python-build

Optional dependencies for the mex bindings: * MATLAB, or * Octave

Optional dependencies for the AMPL bindings: * The AMPL solver library ASL

Optional dependencies for the unit tests: * Check

Installation

In order to compile this package, use the following sequence of commands:

mkdir build && cd build cmake .. <OPTIONS> make [make build_tests && make test]

Options

Use the following options to customize the build process:

• SLEQP_ENABLE_UNIT_TESTS: Enables the unit tests (default: On)
• SLEQP_ENABLE_CUTEST: Enables the CUTest suite (default: Off)
• SLEQP_ENABLE_PYTHON: Enables the build of the python bindings (default : On)
• SLEQP_LPS: Set to specify a linear programming library
• SLEQP_FACT: Set to specify a factorization library
• SLEQP_ENABLE_MATLAB_MEX: Enables the build of mex bindings using MATLAB (default : Off)
• SLEQP_ENABLE_OCTAVE_MEX: Enables the build of mex bindings using Octave (default : Off)
• SLEQP_ENABLE_AMPL: Enables the build of the AMPL interface (default: Off)

References

• Byrd, Richard H., et al. "An algorithm for nonlinear optimization using linear programming and equality constrained subproblems." Mathematical Programming 100.1 (2003): 27-48.
• Lenders, Felix, Christian Kirches, and Andreas Potschka. "trlib: A vector-free implementation of the GLTR method for iterative solution of the trust region problem." Optimization Methods and Software 33.3 (2018): 420-449.