Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization

This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraint

A dynamic gradient approach to Pareto optimization with nonsmooth convex objective functions

In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving non-smooth convex objective functions. Our approach is in the line of a previous work where was considered the case of convex di erentiable objective functions. Based on the Yosida regularization of the subdi erential operators involved in the system, we obtain the existence of strong global trajectories. We prove a descent property for each objective function, and the convergence of trajectories to weak Pareto minima. This approach provides a dynamical endogenous weighting of the objective functions. Applications are given to cooperative games, inverse problems, and numerical multiobjective optimization

Optimality and duality for a class of nonsmooth fractional multiobjective optimization problems (Nonlinear Analysis and Convex Analysis)

In this paper, we establish necessary optimality conditions for (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization problem with inequality and equality constraints by employing some advanced tools of variational analysis and generalized differentiation. Sufficient optimality conditions for such solutions to the considered problem are also provided by means of introducing (strictly) convex-affine functions. Along with optimality conditions, we formulate a dual problem to the primal one and explore weak, strong and converse duality relations between them under assumptions of (strictly) convex-affine functions

Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields ((\hyperlink{CUP}{\mathrm{CUP}}) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of (\hyperlink{CUP}{\mathrm{CUP}}) in terms of the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond-Weir-type robust dual problem to the primal problem (\hyperlink{CUP}{\mathrm{CUP}}), and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.Comment: arXiv admin note: substantial text overlap with arXiv:2105.14366, arXiv:2205.0114

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Approximate Optimality Conditions in Fractional Semi-Infinite Multiobjective Optimization (Study on Nonlinear Analysis and Convex Analysis)

This paper is based on the manuscript "Approximate necessary optimality in fractional semi-infinite multiobjective optimization" written by T. Shitkovskaya, Z. Hong, D.S. Kim and G.R. Piao, which was accepted to J. Nonlinear Convex Anal.This paper provides some new results on weak approximate solutions in fractional multiobjective optimization problems. Specifically, we establish necessary optimality conditions of Fritz-John type for a local weakly E-efficient solution in fuzzy form and, by using limiting constraint qualification, we provide necessary optimality conditions of Karush-Kuhn-Tucker type for a weakly E-quasi-efficient solution. To this purpose advanced tools of variational analysis and generalized differentiation are used