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Connectedness of approximate Henig efficient solution set for set-valued optimization problems. (Chinese. English summary) Zbl 1389.90286

Summary: In this paper, we study the topological properties of approximate Henig efficient solution set for set-valued optimization problem. The relations between approximate Henig efficient solution set and Henig efficient solution set are discussed. Moreover, the closedness of approximate Henig efficient solution set is proved and the connectedness of approximate Henig efficient solution set is obtained under the condition that the objective function is a cone-arcwise connected set-valued mapping. As an application of the result, the connectedness of super efficient solution set is given.

MSC:

90C29 Multi-objective and goal programming
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