New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization

Zhenhua Peng and Yihong Xu ()
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Zhenhua Peng: Nanchang University
Yihong Xu: Nanchang University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 1, No 7, 128-140

Abstract: Abstract A new second-order tangent set is introduced, with which a new second-order tangent epiderivative is also introduced for a set-valued map. Applying a separation theorem for convex sets, second-order Fritz John and Kuhn–Tucker necessary optimality conditions are obtained for a point pair to be a weak minimizer of set-valued optimization problem. Under the assumption of lower semicontinuous, a second-order Kuhn–Tucker sufficient optimality condition is obtained for a point pair to be a weak minimizer of set-valued optimization problem.

Keywords: Weak minimizer; Near cone-subconvexlikeness; Set-valued optimization; Cone; 90C29; 90C46; 54C60; 46G05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-1011-1

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