Optimality conditions for robust weak sharp efficient solutions of nonsmooth uncertain multiobjective optimization problems

In this paper, we investigate an uncertain multiobjective optimization problem involving nonsmooth and nonconvex functions. The notion of a (local/global) robust weak sharp efficient solution is introduced. Then, we establish necessary and sufficient optimality conditions for local and/or the robust weak sharp efficient solutions of the considered problem. These optimality conditions are presented in terms of multipliers and Mordukhovich/limiting subdifferentials of the related functions.

Weak Sharp Minima for Interval-Valued Functions and its Primal-Dual Characterizations Using Generalized Hukuhara Subdifferentiability

This article introduces the concept of weak sharp minima (WSM) for convex interval-valued functions (IVFs). To identify a set of WSM of a convex IVF, we provide its primal and dual characterizations. The primal characterization is given in terms of gHdirectional derivatives. On the other hand, to derive dual characterizations, we propose the notions of the support function of a subset of I(R) n and gH-subdifferentiability for convex IVFs. Further, we develop the required gH-subdifferential calculus for convex IVFs. Thereafter, by using the proposed gH-subdifferential calculus, we provide dual characterizations for the set of WSM of convex IVFs.

On optimality conditions for robust weak sharp solution in uncertain optimizations

In this paper, we investigate the robust optimization problem involving nonsmooth and nonconvex real-valued functions. We firstly establish a necessary condition for the local robust weak sharp solution of considered problem under a constraint qualification. These optimality conditions are presented in terms of multipliers and Mordukhovich subdifferentials of the related functions. Then, by employing the robust version of the (KKT) condition, and some appropriate generalized convexity conditions, we also obtain some sufficient conditions for the global robust weak sharp solutions of the problem. In addition, some examples are presented for illustrating or supporting the results.