This paper investigates calculus rules for the limiting Fréchet-subdifferential of infimum value functions of locally Lipschitzian and non-Lipschitzian functions. It is not required that the infimum is attained.

In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition fuzzy form for approximate weakly robust efficient solutions and then establish theorem quasi-efficient of the sense limiting subdifferential by exploiting terms Fréchet subdifferential. Sufficient conditions (w...

In this paper we study necessary optimality conditions for nonsmooth optimization problems with equality, inequality and abstract set constraints. We derive the enhanced Fritz John condition which contains some new information even in the smooth case than the classical enhanced Fritz John condition. From this enhanced Fritz John condition we derive the enhanced Karush-Kuhn-Tucker (KKT) conditio...

In this paper, we present the concept of generalized invexity for vector-valued functions. Also, we consider different kinds of generalized vector variational-like inequality and a vector optimization problem. Some relations between vector variational-like inequalities and a vector optimization problem are established by using the properties of Mordukhovich limiting subdifferential. Acknowledge...

The Mordukhovich subdifferential, being highly important in variational and non-smooth analysis and optimization, often happens to be hard to calculate. We propose a method for computing the Mordukhovich subdifferential of differences of sublinear (DS) functions via the directed subdifferential of differences of convex (DC) functions. We restrict ourselves to the two-dimensional case mainly for...

The space of directed sets is a Banach space in which convex compact subsets of Rn are embedded. Each directed set is visualized as a (nonconvex) subset of Rn, which is comprised of a convex, a concave and a mixed-type part. Following an idea of A. Rubinov, the directed subdifferential of a difference of convex (DC) functions is defined as the directed difference of the corresponding embedded c...

In this paper we study the mathematical program with geometric constraints such that the image of a mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the nonsmooth enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. In the case where the Banach space is a weakly compactly generated Asplun...

In convex programming, characterizations of the solution set in terms of the subdifferential have been investigated by Mangasarian. An invariance property of the subdifferential of the objective function is studied, and as a consequence, characterizations of the solution set by any solution point and any point in the relative interior of the solution set are given. In quasiconvex programming, h...