Exact penalty functions in optimization with unbounded constraint sets

TL;DR

This paper establishes necessary and sufficient conditions for the exactness of penalty functions in optimization problems with unbounded constraints, extending existing results to broader classes of problems.

Contribution

It provides a comprehensive characterization of penalty function exactness for unbounded constraint sets, including cases with locally Lipschitz, semi-algebraic, or polynomial data.

Findings

Conditions for penalty exactness are characterized in terms of objective and residual functions.

Results generalize and improve upon previous literature on penalty functions.

Applicable to problems with unbounded constraint sets and various data types.

Abstract

This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The case where the data of problems is locally Lipschitz, semi-algebraic or non-degenerate polynomials is studied in detail. The conditions are given in terms of properties of the objective and residual functions of the problems in question. The obtained results generalize and improve some known results in the literature on exact penalty functions.