The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

The aim of the present paper is to obtain a number of Kuhn-Tucker type sufficient optimality conditions for a feasible solution to be an efficient solution under the assumptions of the new notions of weak strictly pseudo quasi α-univex, strong pseudo quasi α-univex, and weak strictly pseudo α-univex vector valued functions. We also derive the duality theorems for Mond-Weir and general Mond-Wei...

Abstract In this paper, we introduce a new concept of sets and class functions called E -univex functions, respectively. For an -differentiable function, the -univexity is introduced by generalizing several concepts generalized convexity earlier defined into optimization theory. addition, some properties are investigated. Further, also introduced. Then, sufficiency so-called -Karush–Kuhn–Tucker...

In the paper, a nonconvex quasidifferentiable optimization problem with the inequality constraints is considered. The concept of a univex function with respect to a convex compact set is introduced. Further, the sufficient optimality conditions and several duality results in the sense of Mond-Weir are established for the considered quasidifferentiable optimization problem under assumption that ...

Problems of multiobjective optimization are widespread in mathematical modelling of real world systems for a very broad range of applications. In particular, several classes of multiobjective problems with set and n-set functions have been the subject of several papers in the last few decades. For a historical survey of optimality conditions and duality for programming problems involving set an...

In this paper, we introduce a new class of generalized convex function, namely, α-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinem...

In this paper, a new class of second order ( , )   -univex and second order ( , )   pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order ( , )   univexity and second order pseudo univexity...

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-...