Second-Order Optimality Conditions for Strict Efficiency of Constrained Set-Valued Optimization

S. J. Li (), S. K. Zhu () and X. B. Li ()
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S. J. Li: Chongqing University
S. K. Zhu: Chongqing University
X. B. Li: Chongqing University

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 2, No 10, 534-557

Abstract: Abstract In this paper, we propose several second-order derivatives for set-valued maps and discuss their properties. By using these derivatives, we obtain second-order necessary optimality conditions for strict efficiency of a set-valued optimization problem with inclusion constraints in real normed spaces. We also establish second-order sufficient optimality conditions for strict efficiency of the set-valued optimization problem in finite-dimensional normed spaces. As applications, we investigate second-order sufficient and necessary optimality conditions for a strict local efficient solution of order two of a nonsmooth vector optimization problem with an abstract set and a functional constraint.

Keywords: Asymptotic second-order contingent cone; Second-order derivative; Semidifferentiable; Set-valued optimization; Optimality conditions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-012-0076-8

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