Generalized differentiability for a class of nondifferentiable operators with applications to nonsmooth optimization
Thomas W. Reiland · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1989
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.