运筹学学报 >
2019 , Vol. 23 >Issue 1: 45 - 52
DOI: https://doi.org/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
收稿日期: 2017-03-09
网络出版日期: 2019-03-15
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
Received date: 2017-03-09
Online published: 2019-03-15
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 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.01.005
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.
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