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The aim of this paper is to study the stability of optimal point sets based on the improvement set E by using the scalarization method and the density results. Under the convergence of a sequence of sets in the sense of Wijsman, we derive the convergence of the sets of E-optimal points, weak E-optimal points, E-quasi-optimal points, E-Benson proper optimal points, E-super optimal points and E-strictly optimal points in the sense of Wijsman. Moreover, we obtain the semicontinuity of E-optimal point mapping, weak E-optimal point mapping, E-quasi-optimal point mapping, E-Benson proper optimal point mapping, E-super optimal point mapping and E-strictly optimal point mapping. Finally, we make a new attempt to establish Lipschitz continuity of these E-optimal point mappings under some suitable conditions. [ABSTRACT FROM AUTHOR]

Starting from the innovative ideas of Chicco et al. (Vector optimization problems via improvement sets. J. Optim. Theory Appl. 2011;150:516–529), in this paper, the concepts of improvement set and-efficiency are introduced in a real locally convex Hausdorff topological vector space. Furthermore, some properties of the improvement sets are given and a kind of proper efficiency, named as-Benson proper efficiency, which unifies some proper efficiency and approximate proper efficiency, is proposed via the improvement sets in vector optimization. Moreover, the concept of-subconvexlikeness of set-valued maps is introduced via the improvement sets and an alternative theorem is proved. In the end, some scalarization theorems and Lagrange multiplier theorems of-Benson proper efficiency are established for a vector optimization problem with set-valued maps. [ABSTRACT FROM PUBLISHER]

In this article, some basic characterizations of a non-differentiable η-pseudolinear function are obtained. By means of these basic characterizations, the solution set of the non-differentiable η-pseudolinear extremum problem is characterized. Our study improves naturally and extends some previously known results. [ABSTRACT FROM PUBLISHER]