A Rewriting System for Convex Optimization Problems

TL;DR

This paper presents a modular rewriting system integrated into CVXPY that translates convex optimization problems into solver-compatible forms through analysis and canonicalization, enhancing solver matching and support.

Contribution

It introduces a novel modular rewriting framework with reductions as first-class objects for better problem-to-solver compatibility in convex optimization.

Findings

Implemented in CVXPY 1.0 for convex problems

Supports diverse solver standard forms

Facilitates problem matching to suitable solvers

Abstract

We describe a modular rewriting system for translating optimization problems written in a domain-specific language to forms compatible with low-level solver interfaces. Translation is facilitated by reductions, which accept a category of problems and transform instances of that category to equivalent instances of another category. Our system proceeds in two key phases: analysis, in which we attempt to find a suitable solver for a supplied problem, and canonicalization, in which we rewrite the problem in the selected solver's standard form. We implement the described system in version 1.0 of CVXPY, a domain-specific language for mathematical and especially convex optimization. By treating reductions as first-class objects, our method makes it easy to match problems to solvers well-suited for them and to support solvers with a wide variety of standard forms.