Abstract
In this paper, a characterization of tightly properly efficient solutions of set-valued optimization problem is obtained. The concept of the well-posedness for a special scalar problem is linked with the tightly properly efficient solutions of set-valued optimization problem.
Highlights
One important problem in vector optimization is to find the efficient points of a set
The concept of tightly proper efficiency was introduced by Zaffaroni [8], and he used a special scalar function to characterize the tightly proper efficiency, and obtained some properties of tightly proper efficiency
We study the characterization and wellposedness for tightly proper efficiency in set-valued vector optimization problem
Summary
One important problem in vector optimization is to find the efficient points of a set. As observed by Kuhn, Tucker and later by Geoffrion, some efficient points exhibit certain abnormal properties. To eliminate such abnormal efficient points, various concept of proper efficiency have been introduced. The original concept was introduced by Kuhn and Tucker [1] and Geoffrion [2], and later modified and formulated in a more generalized framework by Borwein [3], Hartley [4], Benson [5], Henig [6], Borwein and Zhuang [7]; see the references there in. We study the characterization and wellposedness for tightly proper efficiency in set-valued vector optimization problem.
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