Xian-Jun Long

Scalarization and pointwise well-posedness for set optimization problems

In this paper, we consider three kinds of pointwise well-posedness for set optimization problems. We establish some relations among the three kinds of pointwise well-posedness. By virtue of a generalized nonlinear scalarization function, we obtain the equivalence relations between the three kinds of pointwise well-posedness for set optimization problems and the well-posedness of three kinds of scalar optimization problems, respectively.

Metric characterizations of α -well-posedness for symmetric quasi-equilibrium problems

The purpose of this paper is to generalize the concept of α-well-posedness to the symmetric quasi-equilibrium problem. We establish some metric characterizations of α-well-posedness for the symmetric quasi-equilibrium problem. Under some suitable conditions, we prove that the α-well-posedness is equivalent to the existence and uniqueness of solution for the symmetric quasi-equilibrium problems. The corresponding concept of α-well-posedness in the generalized sense is also investigated for the symmetric quasi-equilibrium problem having more than one solution. The results presented in this paper generalize and improve some known results in the literature.

Generalized vector variational-like inequalities and nonsmooth vector optimization problems

In this article, we establish some relationships between a solution of generalized vector variational-like inequalities and an efficient solution or a weakly efficient solution to the nonsmooth vector optimization problem under the assumptions of pseudoinvexity or invariant pseudomonotonicity. Our results extend and improve the corresponding results in the literature.

Remark on cone semistrictly preinvex functions

In this paper, we consider the cone semistrictly preinvex function introduced by Peng and Zhu (J Inequal Appl 93532:1–14, 2006). The relationship between cone semistrictly preinvex functions and cone preinvex functions is investigated. A property of the cone semistrictly preinvex function is obtained.

On the stability of solutions for semi-infinite vector optimization problems

This paper is concerned with the stability of semi-infinite vector optimization problems (SVO). Under weak assumptions, we establish sufficient conditions of the Berge-lower semicontinuity and lower Painlev

Some dual characterizations of Farkas-type results for fractional programming problems

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Some characterizations of duality for DC optimization with composite functions

e´–Kuratowski convergence of weak efficient solutions for (SVO) under functional perturbations of both objective functions and constraint sets. Some examples are given to illustrate that our results are new and interesting.

Generalized radial epiderivatives and nonconvex set-valued optimization problems

In the last three decades, the theory of variational analysis provides very effective and powerful techniques for studying a wide class of problems arising in nonlinear equations, optimization problems, economics equilibrium, game theory, complementarity problems, and fixed point problems, as well as other branches of mathematics and engineering sciences. So, the thorough study of both theory and methods about variational inequalities will help us to find new techniques for solving the practical problem. Vector optimization problems have received much attention by many authors due to their extensive applications in many fields such as biology, economics, optimal control, and differential inclusions. Because of the importance and active impact of the variational inequality and the vector optimization problem in the nonlinear analysis and optimization, this special issue, focusing on most recent contributions, includes works on variational inequalities, equilibrium problems and nonexpansive mappings, vector optimization problems and generalized convex functions, robust optimization problems, and optimization problems with applications, which are based on a strict international peer review procedure and our original proposal. A brief review of the papers is given under the following four topics.