A preconditioned Forward-Backward method for partially separable SemiDefinite Programs

TL;DR

This paper introduces semi-decentralized, distributed algorithms based on preconditioned forward-backward splitting for efficiently solving large-scale, decomposable semidefinite programs by exploiting sparsity patterns.

Contribution

It develops novel algorithms utilizing a preconditioned forward-backward method tailored for partially separable SDPs with chordal sparsity, improving convergence and computational efficiency.

Findings

Algorithms converge to the original SDP solution.

Proposed methods outperform existing algorithms in certain benchmarks.

Efficiently handle large-scale, decomposable SDPs with sparsity.

Abstract

We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semidefinite programs (SDPs). We exploit a chordal aggregate sparsity pattern assumption on the original SDP to obtain a set of mutually coupled SDPs defined on positive semidefinite (PSD) cones of reduced dimensions. We show that the proposed algorithms converge to a solution of the original SDP via iterations of reasonable computational cost. Finally, we compare the performances of the two proposed algorithms with respect to others available in the literature.