Modular design

Rewriting

Digital subscriber line

Mathematics

Domain (mathematical analysis)

Algorithm

Mathematical optimization

Regular polygon

Variety (cybernetics)

Mathematical analysis

Optimization problem

Artificial intelligence

Programming language

Class (philosophy)

Geometry

Solver

Computer science

Theoretical computer science

Telecommunications

Journal of Control and Decision

We describe a modular rewriting system for translating optimization problems written in a domain-specific language (DSL) 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 DSL 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.

A rewriting system for convex optimization problems