A class of nonconvex semidefinite programming in which every KKT point is globally optimal

TL;DR

This paper identifies a special class of nonconvex semidefinite programming problems where all KKT points are globally optimal, providing insights into their structure and implications for optimization theory.

Contribution

It introduces a class of nonconvex SDP problems with the property that every KKT point is globally optimal, expanding understanding of nonconvex optimization.

Findings

All KKT points are globally optimal in this class

The property relates to pseudoconvex optimization

Application to eigenfrequency topology optimization

Abstract

We consider a special class of nonconvex semidefinite programming problems and show that every point satisfying the Karush--Kuhn--Tucker (KKT) conditions is globally optimal despite nonconvexity. This property is related to pseudoconvex optimization. This class of problems is motivated by an eigenfrequency topology optimization problem in structural engineering, but is presented in a more general form.