On optimality conditions for some nonsmooth optimization problems over Lp spaces

Jiri V. Outrata, Werner Römisch

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), Humboldt-Universitt zu Berlin (ISSN 0863-0976), 02-4

MSC 2000

49J52 Nonsmooth analysis
90C15 Stochastic programming

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.