Disciplined Multi-Convex Programming
Abstract
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on alternating or cyclic minimization. Multi-convex problems arise in many applications, such as nonnegative matrix factorization, generalized low rank models, and structured control synthesis, to name just a few. In most applications to date the multi-convexity is simple to verify by hand. In this paper we study the automatic detection and verification of multi-convexity using the ideas of disciplined convex programming. We describe an implementation of our proposed method that detects and verifies multi-convexity, and then invokes one of the general solution methods.
Cite
@article{arxiv.1609.03285,
title = {Disciplined Multi-Convex Programming},
author = {Xinyue Shen and Steven Diamond and Madeleine Udell and Yuantao Gu and Stephen Boyd},
journal= {arXiv preprint arXiv:1609.03285},
year = {2016}
}