Automatic Generation of Explicit Quadratic Programming Solvers

TL;DR

This paper presents a method for automatically generating explicit quadratic programming solvers using code generation, enabling fast, transparent solutions for parametrized convex quadratic programs.

Contribution

It introduces CVXPYgen, an automated code generation tool that creates explicit solvers from high-level problem descriptions, improving efficiency and interpretability.

Findings

Successfully implemented in CVXPYgen, part of CVXPY.

Enables offline computation of solution maps for quick online solving.

Potentially improves transparency and reliability of quadratic programming solutions.

Abstract

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.