Standard Article

Bilinear Optimization

  1. Churlzu Lim

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0107

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Lim, C. 2011. Bilinear Optimization. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of North Carolina at Charlotte, Charlotte, North Carolina

Publication History

  1. Published Online: 14 JAN 2011

Abstract

The bilinear optimization (or bilinear programming) problem is a specially structured quadratic programming problem, where two sets of variables have bilinear relationships. Assuming nonempty and bounded feasible regions, we first present useful properties of this problem, and discuss two commonly used solution approaches as well as local search methods. We also illustrate how the bilinear programming formulation is related to two game-theoretic problems, bimatrix game and sequential game. Then, detection of unboundedness of bilinear programming problems is discussed when feasible region(s) are unbounded. Finally, brief remarks on generalized formulations of bilinear program conclude this article.

Keywords:

  • bilinear programming;
  • min-max problem;
  • Tuy cut;
  • implicit enumeration;
  • bimatrix game;
  • sequential game