Canonical Primal-Dual Method for Solving Non-convex Minimization Problems

TL;DR

This paper introduces a primal-dual algorithm based on canonical duality theory to efficiently solve non-convex minimization problems by reformulating them as convex-concave saddle point problems, demonstrating improved performance.

Contribution

The paper develops a novel primal-dual algorithm leveraging canonical duality theory, providing a new approach for non-convex minimization with enhanced efficiency.

Findings

The algorithm successfully solves non-convex problems.

Numerical examples show better performance than existing methods.

The approach unifies SDP and canonical duality theory.

Abstract

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. %It is proved that the popular SDP method is indeed a special case of the canonical duality theory. Numerical examples are illustrated. Comparing with the existing results, the proposed algorithm can achieve better performance.