Regularization Methods for SDP Relaxations in Large Scale Polynomial Optimization

TL;DR

This paper introduces regularization techniques for semidefinite programming relaxations, enabling the solution of large-scale polynomial optimization problems that are infeasible with traditional interior-point methods.

Contribution

It develops regularization methods tailored for block-structured semidefinite programs, allowing large-scale problems to be solved efficiently on standard computers.

Findings

Regularization methods enable solving larger problems than interior-point methods.

Significant computational improvements in handling large-scale polynomial optimization.

Successful application to various numerical examples demonstrating effectiveness.

Abstract

We study how to solve semidefinite programming relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization methods for solving polynomial optimization problems. We describe these methods for semidefinite optimization with block structures, and then apply them to solve large scale polynomial optimization problems. The performance is tested on various numerical examples. By regularization methods, significantly bigger problems could be solved on a regular computer, which is almost impossible by interior point methods.