基于改进集的集值Ekeland变分原理Ekeland′s variational principle via improvement sets for set-valued maps
万轩;张万里;赵克全;
摘要(Abstract):
Ekeland变分原理在最优化理论及应用研究中具有十分重要的作用.利用非线性标量化函数及相应的非凸分离定理建立了基于改进集的集值Ekeland变分原理.新的Ekeland变分原理包含了一些经典的Ekeland变分原理作为其特例.
关键词(KeyWords): 改进集;Ekeland变分原理;集值映射;非线性标量化函数
基金项目(Foundation): 国家自然科学基金(11301574,11271391);; 重庆市基础与前沿研究计划项目(cstc2015jcyj A00027);; 重庆市教委科学技术研究项目(KJ1500303);; 第二批重庆市高等学校青年骨干教师资助计划
作者(Authors): 万轩;张万里;赵克全;
参考文献(References):
- [1]Ekeland I.On the variational principle[J].Journal of Mathematical Analysis and Applications,1974,47(2):324-353.
- [2]Ekeland I.Nonconvex minimization problems[J].Bulletin(New Series)of the American Mathematical Society,1979,1(3):443-474.
- [3]Chen Guangya,Huang Xuexiang,Hou S H.General Ekeland′s variational principle for set-valued mappings[J].Journal of Optimization Theory and Applications,2000,106(1):151-164.
- [4]Ha T X D.Some variants of the Ekeland variational principle for a set-valued map[J].Journal of Optimization Theory and Applications,2005,124(1):187-206.
- [5]Guti′errez C,Jim′enez B,Novo V.A set-valued Ekeland′s variational principle in vector optimization[J].SIAM Journal on Control and Optimization,2008,47(2):883-903.
- [6]Guti′errez C,Jim′enez B,Novo V,et al.Strict approximate solutions in set-valued optimization with applications to the approximate Ekeland variational principle[J].Nonlinear Analysis,2010,73(12):3842-3855.
- [7]Khanh P Q,Quy D N.On generalized Ekeland′s variational principle and equivalent formulations for set-valued mappings[J].Journal of Global Optimization,2011,49(3):381-396.
- [8]Qiu Jinghui.On Ha′s version of set-valued Ekeland′s variational principle[J].Acta Mathematica Sinica,English Series,2012,28(4):717-726.
- [9]Qiu Jinghui.Set-valued quasi-metrics and a general Ekeland′s variational principle in vector optimization[J].SIAM Journal on Control and Optimization,2013,51(2):1350-1371.
- [10]Chicco M,Mignanego F,Pusillo L,et al.Vector optimization problem via improvement sets[J].Journal of Optimization Theory and Applications,2011,150(3):516-529.
- [11]Guti′errez C,Jim′enez B,Novo V.Improvement sets and vector optimization[J].European Journal of Operational Research,2012,223(2):304-311.
- [12]Zhao Kequan,Yang Xinmin,Peng Jianwen.Weak E-optimal solution in vector optimization[J].Taiwanese Journal of Mathematics,2013,17(4):1287-1302.
- [13]Zhao Kequan,Yang Xinmin.E-Benson proper efficiency in vector optimization[J].Optimization,2015,64(4):739-752.
- [14]Zhao Kequan,Yang Xinmin.A unified stability result with perturbations in vector optimization[J].Optimization Letters,2013,7(8):1913-1919.