Nonsmooth analysis and optimization on partially ordered vector spaces (Q1186331)

The author introduces a broad class of Lipschitz-type operators, called interval-Lipschitz mappings. It is shown that several other classes of mappings in the context of nonsmooth analysis and/or optimization, such as strictly differentiable mappings, convex mappings and sublinear mappings, are special cases of interval-Lipschitz mappings. The generalized directional derivative and the subdifferential of an interval-Lipschitz mapping are defined and several properties of them are derived. A few first-order optimality conditions are established for nonsmooth nonconvex programs. The author also relates these conditions to other optimality conditions involving Lipschitz operators and quasidifferentiable functions. A feature of the optimality conditions in this paper is that they allow for an infinite-dimensional equality constraint.