Robust global optimization with polynomials
成果类型：
Article
署名作者：
Lasserre, JB
署名单位：
Centre National de la Recherche Scientifique (CNRS)
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-005-0687-z
发表日期：
2006
页码：
275-293
关键词：
摘要：
We consider the optimization problems max (z is an element of Omega) min (x is an element of K) p(z, x) and min (x is an element of K) max (z is an element of Omega) p(z, x) where the criterion p is a polynomial, linear in the variables z, the set Omega can be described by LMIs, and K is a basic closed semi-algebraic set. The first problem is a robust analogue of the generic SDP problem max (z is an element of Omega) p(z), whereas the second problem is a robust analogue of the generic problem min (x is an element of K) p(x) of minimizing a polynomial over a semi-algebraic set. We show that the optimal values of both robust optimization problems can be approximated as closely as desired, by solving a hierarchy of SDP relaxations. We also relate and compare the SDP relaxations associated with the max-min and the min-max robust optimization problems.
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