‎we consider nonconvex vector optimization problems with variable ordering structures in banach spaces‎. ‎under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

there are many numerous methods for solving large-scale problems in which some of them are very flexible and efficient in both linear and non-linear cases. league championship algorithm is such algorithm which may be used in the mentioned problems. in the current paper, a new play-off approach will be adapted on league championship algorithm for solving large-scale problems. the proposed algori...

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 recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

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In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.