Fast implementation for semidefinite programs with positive matrix completion

TL;DR

This paper introduces a novel factorization and multithreaded approach to significantly accelerate the solution of semidefinite programs by exploiting sparsity and parallel computing.

Contribution

It proposes a new inverse-based factorization method and parallel implementation to improve the efficiency of the matrix-completion primal-dual interior-point method for SDPs.

Findings

Reduced computation time for sparse SDPs

Effective utilization of multithreaded parallel computing

Enhanced performance of the MC-PDIPM algorithm

Abstract

Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by factorizing the variable matrices. In this paper, we propose a new factorization based on the inverse of the variable matrix to enhance the performance of MC-PDIPM. We also use multithreaded parallel computing to deal with the major bottlenecks in MC-PDIPM. Numerical results show that the new factorization and multithreaded computing reduce the computation time for SDPs that have structural sparsity.