We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraints functions need not to be locally Lipschitz. Using Abadie's constraint qualification and convexificators, we provide  Karush-Kuhn-Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions  under the asymptotic convexity assumption.

We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and Minty types of vector variational inequalities involving Clarke's generalized Jacobians. We also establish the relationship between local quasi weak efficient solutions and vector critical points.

In combining the value function approach and tangential subdifferentials, we establish  necessary optimality conditions of  a nonsmooth multiobjective bilevel programming problem under a suitable constraint qualification. The upper level objectives and constraint functions are neither assumed to be necessarily locally Lipschitz nor convex.

We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing a suitable constraint qualification, we formulate both necessary and sufficient optimality conditions for (local) quasi efficient solutions in terms of tangential subdifferentials. Furthermore, under generalized convexity assumptions, we state strong, weak and converse duality relations of Wolfe and Mond–Weir types. We give a number of examples to illustrate the new concepts and main results of this paper.

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate LU-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions. Keywords:Interval-valued vector optimization problems; generalized approximate LU-convexity; interval vector variational inequalities; LU-efficient solutions MSC: 90C25; 90C29; 90C30; 90C46; 49J40 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 7 March 2020