Nonsmooth Pseudolinearity

In this paper, we introduce the notion of generalized pseudolinearity for nondifferentiable and nonconvex but locally Lipschitz functions defined on a Banach space. We present some characterizations of generalized pseudolinear functions. The characterizations of the solution set of a convex and nondifferentiable but generalized pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions and pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs and pseudolinear programs.