On Optimality Conditions for Some Nonsmooth Optimization Problems over Lp Spaces |
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Authors: | J. V. Outrata W. Römisch |
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Affiliation: | (1) Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic;(2) Humboldt-University Berlin, Institute of Mathematics, Berlin, Germany |
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Abstract: | The paper deals with the minimization of an integral functional over an Lp space subject to various types of constraints. For such optimization problems, new necessary optimality conditions are derived, based on several concepts of nonsmooth analysis. In particular, we employ the generalized differential calculus of Mordukhovich and the fuzzy calculus of proximal subgradients. The results are specialized to nonsmooth two-stage and multistage stochastic programs.The authors express their gratitude to Boris Mordukhovich (Detroit) for his extensive support during this research and to Marian Fabian (Prague) and Alexander Kruger (Ballarat) for valuable discussions. They are indebted also to two anonymous referees for helpful suggestions.The research of this author was partly supported by Grant 1075005 of the Czech Academy of SciencesThe research of this author was supported by the Deutsche Forschungsgemeinschaft |
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Keywords: | Normal integrands integral functionals normal cones subdifferentials fuzzy calculus coderivatives stochastic programming two-stage programs multistage programs |
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