COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

Seminars

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Algebra Seminar: Algebraic methods in integer programming

2005-04-04

1:10p.m. Neill 106W

Bala Krishnamoorthy

Abstract: An integer program is an optimization problem given in the form min{ c^T x | A x = b, x \in Z^n }, where A is an m x n integer matrix, b,c, and x are integer vectors. In this talk, I will provide a brief overview of the techniques used to solve integer programs which use concepts from algebra and algebraic geometry. Specifically, I will illustrate a geometric Buchberger algorithm proposed by Rekha Thomas which uses the concept of finding a Grobner basis of a toric ideal. Necessary background material will be discussed.