A Norm-Based Exterior Penalty Function Technique for Constrained Optimization

Abstract

In this paper, we propose and investigate a norm-based exterior penalty function

technique for solving constrained optimization problems. The classical quadratic penalty

term is replaced by a norm formulation of the constraint violations, resulting in a

flexible penalty structure in which the penalty parameter is independent of the number

and form of the constraints. The resulting unconstrained optimization problems are

solved using a quasi-Newton method. A collection of benchmark test problems is

examined, and the numerical performance of the proposed technique is reported and

discussed. The results demonstrate that the norm-based penalty approach provides an

effective and practical alternative to traditional exterior penalty methods, particularly

when a limited number of quasi-Newton updates is employed