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On Optimality Conditions for Some Nonsmooth Optimization Problems over Lp Spaces

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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.

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Authors and Affiliations

  1. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    J. V. Outrata

  2. Humboldt-University Berlin, Institute of Mathematics, Berlin, Germany

    W. Römisch

Authors
  1. J. V. Outrata
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  2. W. Römisch
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Additional information

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 Sciences

The research of this author was supported by the Deutsche Forschungsgemeinschaft

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Outrata, J.V., Römisch, W. On Optimality Conditions for Some Nonsmooth Optimization Problems over Lp Spaces. J Optim Theory Appl 126, 411–438 (2005). https://doi.org/10.1007/s10957-005-4724-0

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