This paper studies necessary conditions of weak efficiency of a constrained vector minimization problem with equality and inequality constraints in real linear spaces. These results are obtained under generalized convexity conditions through new alternative theorems and given in linear operator rules form. We present a relaxed subconvexlikeness and generalized subconvexlikeness, and likewise, d...

Convexity and generalized convexity play a central role in mathematical economics, engineering, and optimization theory. Therefore, the research on convexity and generalized convexity is one of the most important aspects in mathematical programming (see [1–4, 6–11] and the references therein). Weir and Mond [7] and Weir and Jeyakumar [6] introduced the definition of preinvexity for the scalar f...

In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LU-optimal solution and generalized Slater constraint qualification (GRSCQ). These shown to be sufficient under convexity. The Wolfe Mond-Weir dual problems over cones convexity assumptions, usual duality results establis...

A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order (F, α, ρ, d)-convexity for second order Mangasarian type and general Mond-Weir type vector duals.

The conditions of relative smoothness and strong convexity were recently introduced for the analysis Bregman gradient methods convex optimization. We introduce a generalized left-pr...

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.

In the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{Kim} and textit{Lee} [W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301] and textit{Tarafdar} [E. Tarafdar, Fixed point theorems i...