Convex Optimization in Julia

TL;DR

This paper introduces Convex, a Julia-based framework that simplifies modeling convex optimization problems, automatically verifies DCP rules, and efficiently selects solvers, streamlining the process for users.

Contribution

It presents a novel convex optimization modeling framework in Julia that automates problem verification and solver selection using multiple dispatch.

Findings

Reduces verification and parsing time through Julia's multiple dispatch

Automatically infers problem structure and solver compatibility

Streamlines convex optimization modeling process

Abstract

This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to infer whether the problem complies with the rules of disciplined convex programming (DCP), and to pass the problem to a suitable solver. These operations are carried out in Julia using multiple dispatch, which dramatically reduces the time required to verify DCP compliance and to parse a problem into conic form. Convex then automatically chooses an appropriate backend solver to solve the conic form problem.