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.

Optimality Conditions Using Convexifactors for a Multiobjective Fractional Bilevel Programming Problem

In this paper, a multiobjective fractional bilevel programming problem is considered and optimality conditions using the concept of convexifactors are established for it. For this purpose, a suitable constraint qualification in terms of convexifactors is introduced for the problem. Further in the paper, notions of asymptotic pseudoconvexity, asymptotic quasiconvexity in terms of convexifactors are given and using them sufficient optimality conditions are derived.

A note on the paper "Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints"

In this work, some counterexamples are given to refute some results in the paper by Kohli (RAIRO-Oper. Res. 53, 1617-1632, 2019). We correct the faulty in some of his results.

Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

Analytical design of controllers for discrete-continuous systems with linear control

The study focuses on a certain kind of discrete-continuous systems (DCS): the linear hybrid DCS with state-dependent coefficients. The authors proposed a problem similar to the analytical design of optimal controllers (ADOC). For this study, we generalized the Krotov sufficient optimality conditions. The paper includes several examples.

Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

ON OPTIMALITY AND DUALITY IN INTERVAL-VALUED VARIATIONAL PROBLEM WITH B-(p,r)-INVEXITY

In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition of B -( p,r )- invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established under B -( p,r )-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for an interval- optimization problem Mond-Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.

Sufficient Optimality Conditions in Bilevel Programming

This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by estimating the tangent cone to the feasible set of the bilevel program in terms of initial problem data. This is done by exploiting several different reformulations of the hierarchical model as a single-level problem. To obtain second-order sufficient optimality conditions, we exploit the so-called value function reformulation of the bilevel optimization problem, which is then tackled with the aid of second-order directional derivatives. The resulting conditions can be stated in terms of initial problem data in several interesting situations comprising the settings where the lower level is linear or possesses strongly stable solutions.