Automatic Generation of Explicit Quadratic Programming Solvers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913906463604736 |
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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 |
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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 |