On Optimality Conditions for Some Nonsmooth Optimization Problems over Lp Spaces

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 differe...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 126; no. 2; pp. 411 - 438
Main Authors: Outrata, J. V., Römisch, W.
Format: Journal Article
Language:English
Published: New York, NY Springer 01.08.2005
Springer Nature B.V
Subjects:
Applied sciences
Calculus
Exact sciences and technology
Fuzzy logic
Hilbert space
Mathematical functions
Mathematical models
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Studies
Proximal
Subgradient optimization
multistage programs
two-stage programs
Functional minimization
Subdifferential
integral functionals
Stochastic programming
Fuzzy logic
coderivatives
fuzzy calculus
Nonsmooth analysis
Normal integrands
Optimality condition
Optimality criterion
normal cones
subdifferentials
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-005-4724-0