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Semi-Infinite Programming

  1. Francisco Guerra-Vázquez1,
  2. Jan-J. Rückmann2

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms1037

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Guerra-Vázquez, F. and Rückmann, J.-J. 2011. Semi-Infinite Programming. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. 1

    Universidad de las Américas, Departamento de Actuaría, Física y Matemáticas, Escuela de Ciencias, Puebla, México

  2. 2

    The University of Birmingham School of Mathematics, Birmingham, UK

Publication History

  1. Published Online: 15 FEB 2011

Abstract

This article presents a short introduction to semi-infinite programming (SIP), which over the last two decades has become a vivid research area in mathematical programming with a wide range of applications. An SIP problem is characterized by infinitely many inequality constraints in a finite-dimensional space. We consider first and second order optimality conditions as well as the reduction approach, which allows a local reduction of an SIP problem to a finite programming problem. Furthermore, we discuss several stability concepts including the strong stability of a stationary point and the structural stability. Finally, we briefly refer to solution methods and generalized semi-infinite programming problems.

Keywords:

  • semi-infinite programming;
  • nonconvex optimization;
  • first and second order optimality conditions;
  • reduction approach;
  • strong stability of a stationary point;
  • structural stability;
  • solution methods;
  • generalized semi-infinite programming