Second-order optimality conditions for cone-subarcwise connected set-valued optimization problems
Acta Mathematicae Applicatae Sinica(2018)
摘要
The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set, respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.
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关键词
cone subarcwise connected set-valued map, generalized contingent epiderivative, global proper efficiency, optimality condition, 90C26, 90C46, 52A01, 54C60
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