A Potential Reduction Method for Canonical Duality, with an Application to the Sensor Network Localization Problem

TL;DR

This paper introduces an interior point potential reduction algorithm for solving large non-convex optimization problems via canonical duality, demonstrating its effectiveness on sensor network localization instances.

Contribution

It presents a novel interior point method based on primal-dual total complementarity for non-convex problems, with proven convergence and practical application.

Findings

Global convergence established under mild assumptions

Numerical results show promising efficiency on sensor network localization

Method demonstrates potential for non-convex duality problems

Abstract

We propose to solve large instances of the non-convex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal-dual total complementarity (Lagrange) function. We establish the global convergence result for the algorithm under mild assumptions and demonstrate the method on instances of the Sensor Network Localization problem. Our numerical results are promising and show the possibility of devising efficient interior points methods for non-convex duality.