期刊
SIAM JOURNAL ON OPTIMIZATION
卷 11, 期 3, 页码 796-817出版社
SIAM PUBLICATIONS
DOI: 10.1137/S1052623400366802
关键词
global optimization; theory of moments and positive polynomials; semidefinite programming
We consider the problem of finding the unconstrained global minimum of a real-valued polynomial p(x) : R-n-->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.
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