Automatic Generation of Explicit Quadratic Programming Solvers

Fuente: arXiv
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Main Authors: Schaller, Maximilian, Arnström, Daniel, Bemporad, Alberto, Boyd, Stephen
Format: Preprint
Published: 2025
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author Schaller, Maximilian
Arnström, Daniel
Bemporad, Alberto
Boyd, Stephen
author_facet Schaller, Maximilian
Arnström, Daniel
Bemporad, Alberto
Boyd, Stephen
contents We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a solver computes the coefficients of the affine functions and the linear inequalities defining the polyhedral regions offline; to solve a problem instance online it simply evaluates this explicit solution map. Potential advantages of an explicit solver over a more general purpose iterative solver can include transparency, interpretability, reliability, and speed. In this paper we describe how code generation can be used to automatically generate an explicit solver from a high level description of a parametrized quadratic program. Our method has been implemented in the open-source software CVXPYgen, which is part of CVXPY, a domain specific language for general convex optimization.
format Preprint
id arxiv_https___arxiv_org_abs_2506_11513
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Automatic Generation of Explicit Quadratic Programming Solvers
Schaller, Maximilian
Arnström, Daniel
Bemporad, Alberto
Boyd, Stephen
Optimization and Control
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a solver computes the coefficients of the affine functions and the linear inequalities defining the polyhedral regions offline; to solve a problem instance online it simply evaluates this explicit solution map. Potential advantages of an explicit solver over a more general purpose iterative solver can include transparency, interpretability, reliability, and speed. In this paper we describe how code generation can be used to automatically generate an explicit solver from a high level description of a parametrized quadratic program. Our method has been implemented in the open-source software CVXPYgen, which is part of CVXPY, a domain specific language for general convex optimization.
title Automatic Generation of Explicit Quadratic Programming Solvers
topic Optimization and Control
url https://arxiv.org/abs/2506.11513