Operations Research Transactions >
2019 , Vol. 23 >Issue 1: 45 - 52
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2019.01.005
Second-order characterizations for local weakly nondominated points with variable ordering structure
Received date: 2017-03-09
Online published: 2019-03-15
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.
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 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.01.005
[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.
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