变序结构局部弱非控点的二阶刻画

doi:10.15960/j.cnki.issn.1007-6093.2019.01.005

运筹学学报 ›› 2019, Vol. 23 ›› Issue (1): 45-52.doi: 10.15960/j.cnki.issn.1007-6093.2019.01.005

变序结构局部弱非控点的二阶刻画

徐义红^*, 梅芳

南昌大学数学系, 南昌 330031

收稿日期:2017-03-09 出版日期:2019-03-15 发布日期:2019-03-15
通讯作者: 徐义红 E-mail:xuyihong@ncu.edu.cn
基金资助:
国家自然科学基金（No.11461044），江西省自然科学基金（No.20151BAB201027）

Second-order characterizations for local weakly nondominated points with variable ordering structure

XU Yihong^*, MEI Fang

Department of Mathematics, Nanchang University, Nanchang 330031, China

Received:2017-03-09 Online:2019-03-15 Published:2019-03-15

摘要/Abstract

摘要：

引进了一种二阶切导数，借助该切导数给出了变序结构集值优化问题取得局部弱非控点的二阶最优性必要条件.在某种特殊情况下，给出了一阶最优性条件.通过修正的Dubovitskij-Miljutin切锥导出的约束规格，给出了两个集值映射之和的二阶相依切导数的关系式，进一步得到目标函数与变锥函数的二阶相依切导数分开形式的最优性必要条件.

关键词: 变序结构, 局部弱非控点, 二阶切导数

Abstract:

A kind of second-order tangent derivatives is introduced, with which a second-order necessary optimality condition is established for set-valued optimization with variable ordering structure in the sense of local weakly nondominated points. Under special circumstances, a first-order necessary optimality condition is obtained. The relationship to second-order contingent tangent derivatives for the sum of two set-valued maps is given under some constraint qualification indued by modified Dubovitskij-Miljutin tangent cones. Further more, a necessary optimality condition is obtained where the objective and constraining functions are considered separately with respect to second-order contingent tangent derivatives.

Key words: variable ordering structure, local weakly nondominated point, secondorder tangent derivative

中图分类号:

O221.6

徐义红, 梅芳. 变序结构局部弱非控点的二阶刻画[J]. 运筹学学报, 2019, 23(1): 45-52.

XU Yihong, MEI Fang. Second-order characterizations for local weakly nondominated points with variable ordering structure[J]. Operations Research Transactions, 2019, 23(1): 45-52.

参考文献

[1] Yu P L. Multiple-Criteria Decision Making:Concepts, Techniques, and Extensions[M]. New York:Plenum Press, 1985.
[2] Chen G Y, Yang X Q. Characterizations of variable domination structures via nonlinear scalarization[J]. Journal of Optimization Theory and Applications, 2002, 112(1):97-110.
[3] Durea M, Strugariu R, Tammer C. On set-valued optimization problems with variable ordering structure[J]. Journal of Global Optimization, 2015, 61:745-767.
[4] Jahn J, Khan A A, Zeilinger P. Second-order optimality conditions in set optimization[J]. Journal of Optimization Theory and Applications, 2005, 125:331-347.
[5] Li S K, Teo K L, Yang X Q. Higher-order optimality conditions for set-valued optimization[J]. Journal of Optimization Theory and Applications, 2008, 137:533-553.
[6] Li S J, Zhu S K, Teo K L. Second-order Karush-Kuhn-Tucker optimality conditions for setvalued optimization[J]. Journal of Global Optimization, 2014, 58:673-692.
[7] Khanh P Q, Tung N M. Second-order conditions for open-cone minimizers and firm minimizers in set-valued optimization subject to mixed constraints[J]. Journal of Optimization Theory and Applications, 2016, 171:45-69.
[8] Nguyen Q H, Nguyen V T. New second-order optimality conditions for a class of differentiable optimization problems[J]. Journal of Optimization Theory and Applications, 2016, 171:27-44.
[9] Xu Y H, Li M, Peng Z H. A note on "Higher-order optimality in set-valued optimization using Studniarski derivatives and applications to duality"[Positivity. 18, 449-473(2014)] [J]. Positivity, 2016, 20:295-298.
[10] Peng Z H, Xu Y H. New second-order tangent epiderivatives and applications to set-valued optimization[J]. Journal of Optimization Theory and Applications, 2017, 172(1):128-140.
[11] Gutierrez C, Huerga L, Novo V, et al. Duality related to approximate proper solutions of vector optimization problems[J]. Journal of Global Optimization, 2016, 64:117-139.
[12] Aubin J P, Frankowska H. Set-Valued Analysis[M]. Birkhauser:Boston Massachusetts, 1990.
[13] Li S J, Zhu S K, Teo K L. New generalized second-order contingent epidervatives and set-valued optimization problems[J]. Journal of Optimization Theory and Applications, 2012, 152:587-604.
[14] Shi D S. Contingent derivatives of the perturbation map in multiobjective optimization[J]. Journal of Optimization Theory and Applications, 1991, 70(2):385-396.

变序结构局部弱非控点的二阶刻画

Second-order characterizations for local weakly nondominated points with variable ordering structure

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