Real ideal and the duality of semidefinite programming for polynomial optimization

Details Real ideal and the duality of semidefinite programming for polynomial optimization Real ideal and the duality of semidefinite programming for polynomial optimization

2009-01-20

arxiv.org/abs/0901.2998v2

Mathematics

Optimization and Control

15 pages, 1 figure

Scientific paper

We study the ideal generated by polynomials vanishing on a semialgebraic set and propose an algorithm to calculate the generators, which is based on some techniques of the cylindrical algebraic decomposition. By applying these, polynomial optimization problems with polynomial equality constraints can be modified equivalently so that the associated semidefinite programming relaxation problems have no duality gap. Elementary proofs for some criteria on reality of ideals are also given.

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