Disciplined Biconvex Programming

TL;DR

Disciplined Biconvex Programming (DBCP) provides a user-friendly framework for modeling and automatically solving biconvex optimization problems by extending disciplined convex programming principles, simplifying implementation and experimentation.

Contribution

We introduce DBCP, a framework that automates the transformation of biconvex problems into convex subproblems, enabling easier modeling and solution without extensive convex optimization expertise.

Findings

Automated splitting of biconvex problems into convex subproblems.

Implementation of DBCP as an extension to CVXPY.

Facilitates rapid experimentation with biconvex formulations.

Abstract

We introduce disciplined biconvex programming (DBCP), a modeling framework for specifying and solving biconvex optimization problems. Biconvex optimization problems arise in various applications, including machine learning, signal processing, computational science, and control. Solving a biconvex optimization problem in practice usually resolves to heuristic methods based on alternate convex search (ACS), which iteratively optimizes over one block of variables while keeping the other fixed, so that the resulting subproblems are convex and can be efficiently solved. However, designing and implementing an ACS solver for a specific biconvex optimization problem usually requires significant effort from the user, which can be tedious and error-prone. DBCP extends the principles of disciplined convex programming to biconvex problems, allowing users to specify biconvex optimization problems in a natural way based on a small number of syntax rules. The resulting problem can then be automatically split and transformed into convex subproblems, for which a customized ACS solver is then generated and applied. DBCP allows users to quickly experiment with different biconvex problem formulations, without expertise in convex optimization. We implement DBCP into the open source Python package dbcp, as an extension to the famous domain specific language CVXPY for convex optimization.