Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization

Details Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization

2009-09-04

arxiv.org/abs/0909.0808v1

IMA Volumes in Mathematics and its Applications, 2012, Volume 154, Part 7, 447-481

Mathematics

Optimization and Control

28 pages, survey paper

Scientific paper

10.1007/978-1-4614-1927-3_16

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear algebra or semidefinite programming relaxations of many kinds of feasibility or optimization questions. We are particularly interested in problems arising in combinatorial optimization.

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