Journal of Optimization Theory and Applications

, Volume 126, Issue 2, pp 411–438 | Cite as

On Optimality Conditions for Some Nonsmooth Optimization Problems over L p Spaces

  • J. V. Outrata
  • W. Römisch
Article

Abstract

The paper deals with the minimization of an integral functional over an L p 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.

Keywords

Normal integrands integral functionals normal cones subdifferentials fuzzy calculus coderivatives stochastic programming two-stage programs multistage programs 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • J. V. Outrata
    • 1
  • W. Römisch
    • 2
  1. 1.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPragueCzech Republic
  2. 2.Humboldt-University BerlinInstitute of MathematicsBerlinGermany

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