An approach to vector subdifferentials
- 1 January 1996
- journal article
- research article
- Published by Taylor & Francis in Optimization
- Vol. 38 (3) , 237-251
- https://doi.org/10.1080/02331939608844251
Abstract
A vector subdifferential is constructed for various classes of Lipschitz vector functions on Banach spaces. The existence is proved by compactness arguments, not needing explicit construction of sequences. This subdifferential agrees with some definitions of Thibault and Xu, but appears to be more widely applicable. An application is given to semi-infinite programmingKeywords
This publication has 14 references indexed in Scilit:
- A Fritz John optimality condition using the approximate subdifferentialJournal of Optimization Theory and Applications, 1994
- First order approximations to nonsmooth mappings with application to metric regularityNumerical Functional Analysis and Optimization, 1994
- The smooth variational principle and generic differentiabilityBulletin of the Australian Mathematical Society, 1991
- A class of null sets associated with convex functions on Banach spacesBulletin of the Australian Mathematical Society, 1990
- Differentiability of Lipschitz functions on Banach spacesJournal of Functional Analysis, 1990
- Nonsmooth analysis of vector-valued mappings with contributions to nondifferentiable programmingNumerical Functional Analysis and Optimization, 1986
- Nonsmooth analysis on partially ordered vector spaces. I. Convex casePacific Journal of Mathematics, 1983
- Continuity and Differentiability Properties of Convex OperatorsProceedings of the London Mathematical Society, 1982
- Nonsmooth analysis: differential calculus of nondifferentiable mappingsTransactions of the American Mathematical Society, 1981
- Gaussian null sets and differentiability of Lipschitz map on Banach spacesPacific Journal of Mathematics, 1978