# BARRIER FUNCTIONS AND THEIR MODIFICATIONS

Reference work entry

First Online:

**DOI:**https://doi.org/10.1007/1-4020-0611-X_57

## INTRODUCTION

In the mid-1950s and the early 1960s, Frisch (1955) and Carroll (1961) proposed the use of *Barrier Functions* (BFs) for constrained optimization. Since then, the BFs have been extensively studied, with particularly major work in the area due to Fiacco and McCormick (1968) who developed the Sequential Unconstrained Minimization Technique (SUMT). Currently, methods based on barrier functions make up a considerable part of modern optimization theory.

## BARRIER FUNCTIONS

Consider the constrained optimization problem

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