Second-Order Composed Radial Derivatives of the Benson Proper Perturbation Map for Parametric Multi-Objective Optimization Problems

Qilin Wang and Xiaoyan Zhang ()
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Qilin Wang: College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P. R. China
Xiaoyan Zhang: College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 04, 1-18

Abstract: In this paper, we introduce second-order composed radial derivatives of set-valued maps and establish some of its properties. By applying this second-order derivative, we obtain second-order sensitivity results for parametric multi-objective optimization problems under the Benson proper efficiency without assumptions of cone-convexity and Lipschitz continuity. Some of our results improve and derive the recent corresponding ones in the literature.

Keywords: Parametric multi-objective optimization problems; sensitivity analysis; second-order composed radial derivatives; Benson proper perturbation maps (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920400114

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