Global Optimization with Polynomials and the Problem of Moments (2001)
| Venue: | SIAM Journal on Optimization |
| Citations: | 220 - 26 self |
BibTeX
@ARTICLE{Lasserre01globaloptimization,
author = {Jean B. Lasserre},
title = {Global Optimization with Polynomials and the Problem of Moments},
journal = {SIAM Journal on Optimization},
year = {2001},
volume = {11},
pages = {796--817}
}
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Abstract
We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems. A notion of Karush--Kuhn--Tucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided. Key words. global optimization, theory of moments and positive polynomials, semidefinite programming AMS subject classifications. 90C22, 90C25 PII. S1052623400366802 1.
