Disciplined Biconvex Programming
This work addresses a practical bottleneck for researchers and practitioners in fields like machine learning and signal processing by providing an automated framework for biconvex optimization, though it is incremental as it extends existing disciplined convex programming principles.
The paper tackles the challenge of specifying and solving biconvex optimization problems, which often require manual effort for heuristic methods like alternate convex search, by introducing disciplined biconvex programming (DBCP) to automate problem splitting and solver generation, resulting in an open-source Python package that enables quick experimentation without convex optimization expertise.
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.