# Disciplined Multi-Convex Programming

arXiv: https://arxiv.org/abs/1609.03285 · HTML: https://mlsanity.com/paper/1609.03285/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2016.

## Built on by (most cited first, 6 of 6)

- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization](https://mlsanity.com/paper/2210.15393/) (2022)
- [Disciplined Biconvex Programming](https://mlsanity.com/paper/2511.01813/) (2025)
- [Multi-convex Programming for Discrete Latent Factor Models Prototyping](https://mlsanity.com/paper/2504.01431/) (2025)
- [Fitting Reinforcement Learning Model to Behavioral Data under Bandits](https://mlsanity.com/paper/2511.04454/) (2025)
- [Disciplined Bilevel Programming](https://mlsanity.com/paper/2609.00644/) (2026)

## Abstract (arXiv)

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.