Smooth Exact Penalty Functions: A General Approach

TL;DR

This paper introduces a new perspective on smooth exact penalty functions for constrained optimization, utilizing parametric optimization to establish general conditions for their local and global exactness.

Contribution

It provides a novel approach to analyzing the exactness of Huyer and Neumaier's penalty function, including new proofs and conditions that generalize previous results.

Findings

New simple proof of local exactness

Necessary and sufficient conditions for global exactness

Generalization of existing results in penalty function theory

Abstract

In this article we present a new perspective on the smooth exact penalty function proposed by Huyer and Neumaier that is becoming more and more popular tool for solving constrained optimization problems. Our approach to Huyer and Neumaier's exact penalty function allows one to apply previously unused tools (namely, parametric optimization) to the study of the exactness of this function. We give a new simple proof of the local exactness of Huyer and Neumair's penalty function that significantly generalizes all similar results existing in the literature. We also obtain new necessary and sufficient conditions for the global exactness of this penalty function.