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Efficient algorithms for solving rank two and rank three bilinear programming problems

✍ Scribed by Yasutoshi Yajima; Hiroshi Konno

Publisher: Springer US
Year: 1991
Tongue: English
Weight: 866 KB
Volume: 1
Category: Article
ISSN: 0925-5001
DOI: 10.1007/bf00119989

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✦ Synopsis

Finitely convergent algorithms for solving rank two and three bilinear programming problems are proposed. A rank k bilinear programming problem is a nonconvex quadratic programming problem with the following structure: minimize c& + df,y + i c;x-d;y(xEX, yEY , j=l I

where XC R"' and Y C RnZ are non-empty and bounded polytopes. We show that a variant of parametric simplex algorithm can solve large scale rank two bilinear programming problems efficiently. Also, we show that a cutting-cake algorithm, a more elaborate variant of parametric simplex algorithm can solve medium scale rank three problems.

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