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 variou...

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-...

In this paper, we introduce three new types of generalized convex functions, called semi E-pseudoinvex, strictly semi Epseudoinvex and semi E-quasiinvex functions. Then some of their basic properties are studied, We used directional derivative and obtain the new results in this class of functions. As applications of our results, we obtain optimal solutions for multiobjective programming. AMS Su...

A new class of functions namely, second order strongly F-pseudoconvex functions is introduced which is a generalization of both strongly pseudoconvex functions and strongly pseudoinvex functions. Second order optimality conditions and second order duality results for a class of nonlinear non-differentiable scalar programming problems with a square root term in the objective function as well as ...

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

In this paper we obtain secondand first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints. In the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable. We introduce notions of KTSP-invex problem and second-order KTSP-invex one. We obtain that t...

In this paper by using the scalarization method, we consider Stamppachia variational-like inequalities in terms of normal subdifferential for set-valued maps and study their relations with set-valued optimization problems. Furthermore, some characterizations of the solution sets of K-pseudoinvex extremum problems are given.