含参集值向量均衡问题近似解映射的Lipschitz连续性
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摘要
在赋范线性空间中研究了含参集值向量均衡问题.在引入含参集值向量均衡问题近似有效解的基础上,讨论了含参集值向量均衡问题近似解映射的Lipschitz连续性.借助标量化方法,得到了含参集值向量均衡问题近似解映射的Lipschitz连续的充分性定理.作为应用,研究了含参集值向量优化问题近似解映射的Lipschitz连续性,给出了含参集值向量优化问题近似解映射的Lipschitz连续的充分性条件.
The parametric set-valued vector equilibrium problems are studied in normed linear space.On the basis of introducing the approximate efficient solution of parametric set-valued vector equilibrium problems, the Lipschitz continuity of approximate solution mapping for parametric set-valued vector equilibrium problems is discussed.Sufficient theorem of the Lipschitz continuity of the approximate solution mapping for parametric set-valued vector equilibrium problems is established by using a scalarization method. As applications of these results, the Lipschitz continuity of approximate solution mapping for parametric set-valued vector optimization problem is studied, and sufficient conditions of the Lipschitz continuity of approximate solution mapping for parametric set-valued vector optimization problem are gained.
The parametric set-valued vector equilibrium problems are studied in normed linear space.On the basis of introducing the approximate efficient solution of parametric set-valued vector equilibrium problems, the Lipschitz continuity of approximate solution mapping for parametric set-valued vector equilibrium problems is discussed.Sufficient theorem of the Lipschitz continuity of the approximate solution mapping for parametric set-valued vector equilibrium problems is established by using a scalarization method. As applications of these results, the Lipschitz continuity of approximate solution mapping for parametric set-valued vector optimization problem is studied, and sufficient conditions of the Lipschitz continuity of approximate solution mapping for parametric set-valued vector optimization problem are gained.
引文
[1] LI X B,LI S J,CHEN C R.Lipschitz continuity of an approximate solution mapping to equilibrium problems [J].Taiwanese Journal of Mathematics,2012,16(3):1027-1040.
[2] ANH L Q,KHANH P Q,TAM T N.On H?lder continuity of approximate solutions to parametric equilibrium problems [J].Nonlinear Analysis,2012,75(4):2293-2303.
[3] SADEQI I,SALEHI PAYDAR M.Lipschitz continuity of an approximate solution mapping for parametric set-valued vector equilibrium problems [J].Optimization,2016,65(5):1003-1021.
[4] PENG Zaiyun,YANG Xinmin,TEO K L.On the H?lder continuity of approximate solution mappings to parametric weak generalized Ky Fan inequality [J].Journal of Industrial and Management Optimization,2015,11(2):549-562.
[5] ANH L Q,NGUYEN K T,TAM T N.On H?lder continuity of approximate solution maps to vector equilibrium problems [J].Turkish Journal of Mathematics,2017,41(5):1591-1607.
[6] LI S J,CHEN C R,LI X B,et al.H?lder continuity and upper estimates of solutions to vector quasiequilibrium problems [J].European Journal of Operational Research,2011,210(2):148-157.
[7] ANH L Q,KHANH P Q.On the H?lder continuity of solutions to parametric multivalued vector equilibrium problems [J].Journal of Mathematical Analysis and Applications,2006,321(1):308-315.
[8] ANH L Q,KHANH P Q.Uniqueness and H?lder continuity of the solution to multivalued vector equilibrium problems in metric spaces [J].Journal of Global Optimization,2007,37(3):449-465.
[9] ANH L Q,KHANH P Q.Sensitivity analysis for multivalued quasiequilibrium problems in metric spaces:H?lder continuity of solutions [J].Journal of Global Optimization,2008,42(4):515-531.
[10] ANH L Q,KHANH P Q.H?lder continuity of the unique solution to quasiequilibrium problems in metric spaces [J].Journal of Optimization Theory and Applications,2009,141(1):37-54.
[11] LI S J,LI X B.H?lder continuity of solutions to parametric weak generalized Ky Fan inequality [J].Journal of Optimization Theory and Applications,2011,149(3):540-553.
[12] LI X B,LONG X J,ZENG J.H?lder continuity of the solution set of the Ky Fan inequality [J].Journal of Optimization Theory and Applications,2013,158(2):397-409.
[13] CHEN C R.H?lder continuity of the unique solution to parametric vector quasiequilibrium problems via nonlinear scalarization [J].Positivity,2013,17(1):133-150.
[14] CHEN C R,LI M H.H?lder continuity of solutions to parametric vector equilibrium problems with nonlinear scalarization [J].Numerical Functional Analysis and Optimization,2014,35(6):685-707.
[15] CHEN C R,LI L L,LI M H.H?lder continuity results for nonconvex parametric generalized vector quasiequilibrium problems via nonlinear scalarizing functions [J].Optimization,2016,65(1):35-51.
[16] HAN Yu.Lipschitz continuity of approximate solution mappings to parametric generalized vector equilibrium problems [J].Journal of Optimization Theory and Applications,2018,178(3):763-793.
[17] KURATOWSKI K.Topology:vol 1 and 2 [M].New York:Academic Press,1968.
[18] HAN Yu,HUANG Ningjing.Some characterizations of the approximate solutions to generalized vector equilibrium problems [J].Journal of Industrial and Management Optimization,2016,12(5):1135-1151.
[2] ANH L Q,KHANH P Q,TAM T N.On H?lder continuity of approximate solutions to parametric equilibrium problems [J].Nonlinear Analysis,2012,75(4):2293-2303.
[3] SADEQI I,SALEHI PAYDAR M.Lipschitz continuity of an approximate solution mapping for parametric set-valued vector equilibrium problems [J].Optimization,2016,65(5):1003-1021.
[4] PENG Zaiyun,YANG Xinmin,TEO K L.On the H?lder continuity of approximate solution mappings to parametric weak generalized Ky Fan inequality [J].Journal of Industrial and Management Optimization,2015,11(2):549-562.
[5] ANH L Q,NGUYEN K T,TAM T N.On H?lder continuity of approximate solution maps to vector equilibrium problems [J].Turkish Journal of Mathematics,2017,41(5):1591-1607.
[6] LI S J,CHEN C R,LI X B,et al.H?lder continuity and upper estimates of solutions to vector quasiequilibrium problems [J].European Journal of Operational Research,2011,210(2):148-157.
[7] ANH L Q,KHANH P Q.On the H?lder continuity of solutions to parametric multivalued vector equilibrium problems [J].Journal of Mathematical Analysis and Applications,2006,321(1):308-315.
[8] ANH L Q,KHANH P Q.Uniqueness and H?lder continuity of the solution to multivalued vector equilibrium problems in metric spaces [J].Journal of Global Optimization,2007,37(3):449-465.
[9] ANH L Q,KHANH P Q.Sensitivity analysis for multivalued quasiequilibrium problems in metric spaces:H?lder continuity of solutions [J].Journal of Global Optimization,2008,42(4):515-531.
[10] ANH L Q,KHANH P Q.H?lder continuity of the unique solution to quasiequilibrium problems in metric spaces [J].Journal of Optimization Theory and Applications,2009,141(1):37-54.
[11] LI S J,LI X B.H?lder continuity of solutions to parametric weak generalized Ky Fan inequality [J].Journal of Optimization Theory and Applications,2011,149(3):540-553.
[12] LI X B,LONG X J,ZENG J.H?lder continuity of the solution set of the Ky Fan inequality [J].Journal of Optimization Theory and Applications,2013,158(2):397-409.
[13] CHEN C R.H?lder continuity of the unique solution to parametric vector quasiequilibrium problems via nonlinear scalarization [J].Positivity,2013,17(1):133-150.
[14] CHEN C R,LI M H.H?lder continuity of solutions to parametric vector equilibrium problems with nonlinear scalarization [J].Numerical Functional Analysis and Optimization,2014,35(6):685-707.
[15] CHEN C R,LI L L,LI M H.H?lder continuity results for nonconvex parametric generalized vector quasiequilibrium problems via nonlinear scalarizing functions [J].Optimization,2016,65(1):35-51.
[16] HAN Yu.Lipschitz continuity of approximate solution mappings to parametric generalized vector equilibrium problems [J].Journal of Optimization Theory and Applications,2018,178(3):763-793.
[17] KURATOWSKI K.Topology:vol 1 and 2 [M].New York:Academic Press,1968.
[18] HAN Yu,HUANG Ningjing.Some characterizations of the approximate solutions to generalized vector equilibrium problems [J].Journal of Industrial and Management Optimization,2016,12(5):1135-1151.