A predictor-corrector algorithm for semidefinite programming that uses the factor width cone

TL;DR

This paper introduces a novel interior point method for semidefinite programming that operates within the factor width cone, enhancing parallelization and providing theoretical convergence guarantees.

Contribution

It presents a new predictor-corrector algorithm for SDPs that works in the factor width cone, differing from traditional matrix-based approaches.

Findings

Proves global convergence of the proposed method

Provides complexity analysis of the algorithm

Demonstrates suitability for parallel computation

Abstract

We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed algorithm works in the cone of matrices of constant \emph{factor width}. This adaptation makes the proposed method more suitable for parallelization than the standard IPM. We prove global convergence and provide a complexity analysis. Our work is inspired by a series of papers by Ahmadi, Dash, Majumdar and Hall, and builds upon a recent preprint by Roig-Solvas and Sznaier [arXiv:2202.12374, 2022].