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Global optimization in problems with uncertainties

โœ Scribed by Efim A. Galperin

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
317 KB
Volume
47
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

Problems with uncertainties can be viewed and formalized making use of multifunctions or general set-valued functions which are usually non-differentiable. A new concept of global optimality is proposed which allows us to solve global optimization problems with uncertainties, in natural setting without imposing artificial constraints on uncertainties, nor introducing a kind of partial ordering (in order to apply conventional optimality concepts and optimization techniques), nor considering solution ยซin probabilityยป. With the new concept, deterministic optimization requires two optimization procedures. Preliminary study of the subject is presented with many illustrative examples. Then, a monotonic iterative algorithm is developed which renders approximate solutions with a precision specified in advance. ({ }^{1})

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## Abstract Two novel deterministic global optimization algorithms for nonconvex mixedโ€integer problems (MINLPs) are proposed, using the advances of the ฮฑBB algorithm for nonconvex NLPs of Adjiman et al. The special structure mixedโ€integer ฮฑBB algorithm (SMINโ€ฮฑBB) addresses problems with nonconvexi