Abstract
We study general semi-infinite programming problems (GSIP) from the topological point of view. Introducing the symmetric Mangasarian-Fromovitz constraint qualification (Sym-MFCQ) for GSIPs, we describe the closure of the GSIP feasible set. It is proved that Sym-MFCQ is stable and generic. Moreover, under Sym-MFCQ, the GSIP feasible set is shown to be a Lipschitz manifold. For GSIPs, we state the nonsmooth symmetric reduction ansatz (NSRA). NSRA is proven to hold generically at all KKT points for the GSIP. NSRA allows us to reduce the GSIP to a so-called disjunctive optimization problem. This reduction enables to establish the critical point theory for GSIPs.
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© 2012 Springer Science+Business Media, LLC
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Shikhman, V. (2012). General Semi-infinite Programming Problems. In: Topological Aspects of Nonsmooth Optimization. Springer Optimization and Its Applications(), vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1897-9_3
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DOI: https://doi.org/10.1007/978-1-4614-1897-9_3
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Online ISBN: 978-1-4614-1897-9
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