Invariant Pseudolinearity with Applications

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions, and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs, and η-pseudolinear programs.