American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Robust univariate cubic $L_2$ splines: Interpolating data with uncertain positions of measurements
  • JIMO Home
  • This Issue
  • Next Article
    On convergence of augmented Lagrangian method for inverse semi-definite quadratic programming problems
April  2009, 5(2): 341-349. doi: 10.3934/jimo.2009.5.341

Well-Posedness for vector quasi-equilibrium problems with applications

Nan-Jing Huang 1, , Xian-Jun Long 2, and  Chang-Wen Zhao 3,

1. 

Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064
2. 

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
3. 

College of Business and Management, Sichuan University, Chengdu, Sichuan 610064, China

Received  March 2008 Revised  September 2008 Published  April 2009

In this paper, we introduce the concept of well-posedness for the vector quasi-equilibrium problem. We obtain some necessary and sufficient conditions for well-posedness of vector quasi-equilibrium problems. As applications, we investigate the well-posedness for vector quasi-variational inequality problems and vector quasi-optimization problems.
Keywords: vector quasi-optimization problem, Vector quasi-equilibrium problem, vector quasi-variational inequality problem, approximating sequence., well-posedness.
Mathematics Subject Classification: Primary: 49K40, 90C3.
Citation: Nan-Jing Huang, Xian-Jun Long, Chang-Wen Zhao. Well-Posedness for vector quasi-equilibrium problems with applications. Journal of Industrial and Management Optimization, 2009, 5 (2) : 341-349. doi: 10.3934/jimo.2009.5.341
[1]

M. H. Li, S. J. Li, W. Y. Zhang. Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems. Journal of Industrial and Management Optimization, 2009, 5 (4) : 683-696. doi: 10.3934/jimo.2009.5.683
[2]

Jingjing Wang, Zaiyun Peng, Zhi Lin, Daqiong Zhou. On the stability of solutions for the generalized vector quasi-equilibrium problems via free-disposal set. Journal of Industrial and Management Optimization, 2021, 17 (2) : 869-887. doi: 10.3934/jimo.2020002
[3]

S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial and Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155
[4]

Jian-Wen Peng, Xin-Min Yang. Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems. Journal of Industrial and Management Optimization, 2015, 11 (3) : 701-714. doi: 10.3934/jimo.2015.11.701
[5]

Kenji Kimura, Yeong-Cheng Liou, Soon-Yi Wu, Jen-Chih Yao. Well-posedness for parametric vector equilibrium problems with applications. Journal of Industrial and Management Optimization, 2008, 4 (2) : 313-327. doi: 10.3934/jimo.2008.4.313
[6]

Yunan Wu, Guangya Chen, T. C. Edwin Cheng. A vector network equilibrium problem with a unilateral constraint. Journal of Industrial and Management Optimization, 2010, 6 (3) : 453-464. doi: 10.3934/jimo.2010.6.453
[7]

Masao Fukushima. A class of gap functions for quasi-variational inequality problems. Journal of Industrial and Management Optimization, 2007, 3 (2) : 165-171. doi: 10.3934/jimo.2007.3.165
[8]

Xinmin Yang. On symmetric and self duality in vector optimization problem. Journal of Industrial and Management Optimization, 2011, 7 (3) : 523-529. doi: 10.3934/jimo.2011.7.523
[9]

Qilin Wang, Shengji Li. Lower semicontinuity of the solution mapping to a parametric generalized vector equilibrium problem. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1225-1234. doi: 10.3934/jimo.2014.10.1225
[10]

Lori Badea. Multigrid methods for some quasi-variational inequalities. Discrete and Continuous Dynamical Systems - S, 2013, 6 (6) : 1457-1471. doi: 10.3934/dcdss.2013.6.1457
[11]

Yusuke Murase, Risei Kano, Nobuyuki Kenmochi. Elliptic Quasi-variational inequalities and applications. Conference Publications, 2009, 2009 (Special) : 583-591. doi: 10.3934/proc.2009.2009.583
[12]

Alexandre Caboussat, Roland Glowinski. Numerical solution of a variational problem arising in stress analysis: The vector case. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1447-1472. doi: 10.3934/dcds.2010.27.1447
[13]

Takeshi Fukao, Nobuyuki Kenmochi. Quasi-variational inequality approach to heat convection problems with temperature dependent velocity constraint. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2523-2538. doi: 10.3934/dcds.2015.35.2523
[14]

Timur Akhunov. Local well-posedness of quasi-linear systems generalizing KdV. Communications on Pure and Applied Analysis, 2013, 12 (2) : 899-921. doi: 10.3934/cpaa.2013.12.899
[15]

Yurii Nesterov, Laura Scrimali. Solving strongly monotone variational and quasi-variational inequalities. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1383-1396. doi: 10.3934/dcds.2011.31.1383
[16]

Nobuyuki Kenmochi. Parabolic quasi-variational diffusion problems with gradient constraints. Discrete and Continuous Dynamical Systems - S, 2013, 6 (2) : 423-438. doi: 10.3934/dcdss.2013.6.423
[17]

Laura Scrimali. Mixed behavior network equilibria and quasi-variational inequalities. Journal of Industrial and Management Optimization, 2009, 5 (2) : 363-379. doi: 10.3934/jimo.2009.5.363
[18]

Yusuke Murase, Atsushi Kadoya, Nobuyuki Kenmochi. Optimal control problems for quasi-variational inequalities and its numerical approximation. Conference Publications, 2011, 2011 (Special) : 1101-1110. doi: 10.3934/proc.2011.2011.1101
[19]

Antonio Algaba, Estanislao Gamero, Cristóbal García. The reversibility problem for quasi-homogeneous dynamical systems. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3225-3236. doi: 10.3934/dcds.2013.33.3225
[20]

Jianfeng Huang, Haihua Liang. Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 861-873. doi: 10.3934/dcdsb.2020145

2021 Impact Factor: 1.411

Tools

Metrics

  • PDF downloads (93)
  • HTML views (0)
  • Cited by (13)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy