On existence and uniqueness of stationary points in semi-infinite optimization |
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Authors: | Jan-J Rückmann |
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Institution: | Technische Universit?t München, Zentrum Mathematik, D-80290 München, Germany?e-mail: rueckman@appl-math.tu-muenchen.de., DE
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Abstract: | The paper deals with semi-infinite optimization problems which are defined by finitely many equality constraints and infinitely
many inequality constraints. We generalize the concept of strongly stable stationary points which was introduced by Kojima
for finite problems; it refers to the local existence and uniqueness of a stationary point for each sufficiently small perturbed
problem, where perturbations up to second order are allowed. Under the extended Mangasarian-Fromovitz constraint qualification
we present equivalent conditions for the strong stability of a considered stationary point in terms of first and second derivatives
of the involved functions. In particular, we discuss the case where the reduction approach is not satisfied.
Received June 30, 1995 / Revised version received October 9, 1998?
Published online June 11, 1999 |
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Keywords: | : semi-infinite optimization – reduction approach – stationary point – strong stability – extended Mangasarian-Fromovitz constraint qualification Mathematics Subject Classification (1991): 90C30 90C31 90C34 49M39 |
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