Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

BARRIER FUNCTIONS AND THEIR MODIFICATIONS

  • Roman A. Polyak
Reference work entry
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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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Roman A. Polyak
    • 1
  1. 1.George Mason UniversityFairfaxUSA