Semicontinuity of the solution set map to a set-valued weak vector variational inequality

Previous Article
Semilocally prequasi-invex functions and characterizations
JIMO Home
This Issue
Next Article
Spline function smooth support vector machine for classification

July 2007, 3(3): 519-528. doi: 10.3934/jimo.2007.3.519

Semicontinuity of the solution set map to a set-valued weak vector variational inequality

1.	College of Mathematics and Science, Chongqing University, Chongqing, 400044, China, China

Received September 2006 Revised December 2006 Published July 2007

Abstract
Related Papers

This paper investigates the semicontinuity of the solution set map for a parametric set-valued weak vector variational inequality in Banach spaces. The upper semicontinuity and closedness of the solution set map are obtained. A parametric gap function is proposed by using a nonlinear scalarization function. By virtue of the parametric gap function and a key assumption, the lower semicontinuity of the solution set map is established.

Keywords: parametric gap function, nonlinear scalarization function, upper semicontinuity, set-valued weak vector variational inequality., Lower semicontinuity.

Mathematics Subject Classification: 90C31, 49J5.

Citation: C. R. Chen, S. J. Li. Semicontinuity of the solution set map to a set-valued weak vector variational inequality. Journal of Industrial & Management Optimization, 2007, 3 (3) : 519-528. doi: 10.3934/jimo.2007.3.519

[1]	Qilin Wang, Shengji Li. Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1225-1234. doi: 10.3934/jimo.2014.10.1225
[2]	Chunrong Chen, Zhimiao Fang. A note on semicontinuity to a parametric generalized Ky Fan inequality. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 779-784. doi: 10.3934/naco.2012.2.779
[3]	Kenji Kimura, Jen-Chih Yao. Semicontinuity of solution mappings of parametric generalized strong vector equilibrium problems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 167-181. doi: 10.3934/jimo.2008.4.167
[4]	Robert Baier, Thuy T. T. Le. Construction of the minimum time function for linear systems via higher-order set-valued methods. Mathematical Control & Related Fields, 2019, 9 (2) : 223-255. doi: 10.3934/mcrf.2019012
[5]	Xing Wang, Nan-Jing Huang. Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces. Journal of Industrial & Management Optimization, 2013, 9 (1) : 57-74. doi: 10.3934/jimo.2013.9.57
[6]	Suxiang He, Pan Zhang, Xiao Hu, Rong Hu. A sample average approximation method based on a D-gap function for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 977-987. doi: 10.3934/jimo.2014.10.977
[7]	Yejuan Wang. On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3669-3708. doi: 10.3934/dcdsb.2016116
[8]	Zengjing Chen, Yuting Lan, Gaofeng Zong. Strong law of large numbers for upper set-valued and fuzzy-set valued probability. Mathematical Control & Related Fields, 2015, 5 (3) : 435-452. doi: 10.3934/mcrf.2015.5.435
[9]	S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155
[10]	Yonghai Wang. On the upper semicontinuity of pullback attractors with applications to plate equations. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1653-1673. doi: 10.3934/cpaa.2010.9.1653
[11]	Micol Amar, Virginia De Cicco. Lower semicontinuity for polyconvex integrals without coercivity assumptions. Evolution Equations & Control Theory, 2014, 3 (3) : 363-372. doi: 10.3934/eect.2014.3.363
[12]	Guolin Yu. Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 35-44. doi: 10.3934/naco.2016.6.35
[13]	Ying Gao, Xinmin Yang, Jin Yang, Hong Yan. Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps. Journal of Industrial & Management Optimization, 2015, 11 (2) : 673-683. doi: 10.3934/jimo.2015.11.673
[14]	Qilin Wang, Liu He, Shengjie Li. Higher-order weak radial epiderivatives and non-convex set-valued optimization problems. Journal of Industrial & Management Optimization, 2019, 15 (2) : 465-480. doi: 10.3934/jimo.2018051
[15]	Jiawei Chen, Zhongping Wan, Liuyang Yuan. Existence of solutions and $\alpha$-well-posedness for a system of constrained set-valued variational inequalities. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 567-581. doi: 10.3934/naco.2013.3.567
[16]	Yonghai Wang, Chengkui Zhong. Upper semicontinuity of pullback attractors for nonautonomous Kirchhoff wave models. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3189-3209. doi: 10.3934/dcds.2013.33.3189
[17]	Ahmed Y. Abdallah. Upper semicontinuity of the attractor for a second order lattice dynamical system. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 899-916. doi: 10.3934/dcdsb.2005.5.899
[18]	María Astudillo, Marcelo M. Cavalcanti. On the upper semicontinuity of the global attractor for a porous medium type problem with large diffusion. Evolution Equations & Control Theory, 2017, 6 (1) : 1-13. doi: 10.3934/eect.2017001
[19]	Zhijian Yang, Yanan Li. Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-14. doi: 10.3934/dcdsb.2019036
[20]	Roger Metzger, Carlos Arnoldo Morales Rojas, Phillipe Thieullen. Topological stability in set-valued dynamics. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1965-1975. doi: 10.3934/dcdsb.2017115

2017 Impact Factor: 0.994

American Institute of Mathematical Sciences