A Unifying Theory of Exactness of Linear Penalty Functions

TL;DR

This paper develops a comprehensive theory of exact linear penalty functions, unifying existing results and providing necessary and sufficient conditions for their exactness, enhancing understanding of penalty techniques.

Contribution

It introduces a unified framework for analyzing exact linear penalty functions and emphasizes necessary conditions for their exactness, advancing theoretical understanding.

Findings

Provides necessary and sufficient conditions for exactness

Unifies various existing results on penalty functions

Deepens understanding of the conditions for penalty exactness

Abstract

In this article we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally exact linear penalty functions, and obtain various necessary and sufficient conditions for the exactness of a linear penalty function. We pay more attention than usual to necessary conditions that allows us to deeper understand the exact penalty technique.