Second-Order M-Composed Tangent Derivative and Its Applications

Yi-Hong Xu () and Zhen-Hua Peng
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Yi-Hong Xu: Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China
Zhen-Hua Peng: Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2018, vol. 35, issue 05, 1-20

Abstract: A new kind of second-order tangent derivative, second-order M-composed tangent derivative, for a set-valued function is introduced with help of a modified Dubovitskij–Miljutin cone. By using the concept, several generalized convex set-valued functions are introduced. When both the objective function and constrained function are second-order M-composed derivable, under the assumption of nearly cone-subconvexlikeness, by applying a separation theorem for convex sets, Fritz John and Kuhn–Tucker second-order necessary optimality conditions are obtained for a point pair to be a weak minimizer of set-valued optimization problem. Under the assumption of generalized pseudoconvexity, a Kuhn–Tucker second-order sufficient optimality condition is obtained for a point pair to be a weak minimizer of set-valued optimization problem. A unified second-order necessary and sufficient optimality condition is derived in terms of second-order M-composed tangent derivatives.

Keywords: Weak minimizer; near cone-subconvexlikeness; set-valued optimization; cone (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S021759591850029X

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