Published Online: 14 JAN 2011
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
Wiley Encyclopedia of Operations Research and Management Science
How to Cite
Lim, C. 2011. Bilinear Optimization. Wiley Encyclopedia of Operations Research and Management Science. .
- Published Online: 14 JAN 2011
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.
- bilinear programming;
- min-max problem;
- Tuy cut;
- implicit enumeration;
- bimatrix game;
- sequential game