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Generalized differentiability for a class of nondifferentiable operators with applications to nonsmooth optimization

Published online by Cambridge University Press:  09 April 2009

Thomas W. Reiland
Thomas W. Reiland
Affiliation:
Department of Statistics and Graduate, Program in Operations Research, North Carolina State University, Box 8203, Raleigh, North Carolina 27695-8203, U.S.A.
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Abstract

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A theory of generalized gradients is presented for a class of Lipschitz vector-valued mappings from a Banach space to a locally convex order complete vector lattice. Necessary optimality conditions are obtained for nonconvex programming problems on Banach spaces with vector- valued operator constraints and/or an arbitrary set constraint. Sufficient optimality conditions are also obtained under mild convexity assumptions.

MSC classification

Secondary: 90C48: Programming in abstract spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 1 , August 1989 , pp. 114 - 132
Copyright
Copyright © Australian Mathematical Society 1989

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