Nonsmooth analysis and optimization on partially ordered vector spaces

Abstract

Interval-Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz-type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice. Sample applications to the theory of nonsmooth optimization are given.

Keywords

• interval-Lipschitz mapping
• subdifferential
• optimality conditions.