J Austral Math Soc Ser A 47 pp114--132, 1989.

Generalized Differentiability for a Class of Nondifferentiable Operators with Applications to Nonsmooth Optimization

Thomas W. Reiland

(Received 10 October 1987; revised 16 March 1988)

Abstract

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.

1980 AMS Subject Classification (1985 Revision): primary 49B27; secondary 90C48

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Authors

Thomas W. Reiland: 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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Last Modified: Wed Feb 19 10:27:51 2003