运筹学学报 >
2021 , Vol. 25 >Issue 1: 73 - 80
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2021.01.006
对称向量拟均衡问题有效解的存在性
收稿日期: 2019-02-19
网络出版日期: 2021-03-05
基金资助
国家自然科学基金(11061023)
An existence theorem for efficient solutions of symmetric vector quasi-equilibrium problems
Received date: 2019-02-19
Online published: 2021-03-05
王秀玲, 龚循华 . 对称向量拟均衡问题有效解的存在性[J]. 运筹学学报, 2021 , 25(1) : 73 -80 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.01.006
In this paper, an existence theorem for efficient solutions of symmetric vector quasi-equilibrium problems is established by using a scalarization method. As applications of the scalarization method, we use the scalarization method to obtain existence theorems for efficient solutions of vector variational inequality and vector quasi-variational inequality.
| 1 | Ansari Q H , Oettli W , Schi$\ddot{\rm{a}}$ger D . A generalization of vectorial equilibria[J]. Mathematical Methods of Operations Research, 1997, 46, 147- 152. |
| 2 | Ansari Q H , Konnov I V , Yao J C . Existence of a solution and variational principles for vector equilibrium problems[J]. Journal of Optimization Theory and Applications, 2001, 110, 481- 492. |
| 3 | Tan N X . On the existence of solutions of quasivariational inclusion problems[J]. Journal of Global Optimization, 2004, 123, 619- 638. |
| 4 | Fang X P , Huang N J . Strong vector variational inequalities in Banach spaces[J]. Applied Mathematics Letters, 2006, 19, 362- 368. |
| 5 | Long X J , Huang N J , Teo K L . Existence and stability of solutions for generalized strong vector quasi-equilibrium problem[J]. Computational Mathematics and Modeling, 2008, 47, 445- 451. |
| 6 | Hou S H , Gong X H , Yang X M . Existence and stability of solutions for generalized $y$ Fan inequality problems with trifunctions[[J]. Journal of Optimization Theory and Applications, 2010, 146, 387- 398. |
| 7 | Cap$\breve{\rm{a}}$t$\breve{\rm{a}}$ A . Existence results for proper efficient solutions of vector equilibrium problems and applications[J]. Journal of Global Optimization, 2011, 51, 657- 675. |
| 8 | Blum E , Oettli W . From optimization and variational inequalities to equilibrium problems[J]. Mathematics Student, 1994, 63, 123- 145. |
| 9 | Noor M A , Oettli W . On general nonlinear complementarity problems and quasiequilibria[J]. Le Matematiche XLLX, 1994, 49, 313- 331. |
| 10 | Fu J Y . Symmetric vector quasi-equilibrium problems[J]. Journal of Mathematical Analysis and Applications, 2003, 285, 708- 713. |
| 11 | Farajzadeh A P . On the symmetric vector quasi-equilibrium problems[J]. Journal of Mathematical Analysis and Applications, 2006, 322, 1099- 1110. |
| 12 | Chen J C , Gong X H . The stability of set of solutions for symmetric vector quasi-equilibrium problems[J]. Journal of Global Optimization, 2008, 136, 359- 374. |
| 13 | Gong X H . Symmetric strong vector quasi-equilibrium problems[J]. Mathematical Methods of Operations Research, 2007, 65, 305- 314. |
| 14 | Tanaka T . Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions[J]. Journal of Optimization Theory and Applications, 1994, 81, 355- 377. |
| 15 | Ferro F . A minimax theorem for vector-valued functions[J]. Journal of Optimization Theory and Applications, 1989, 60, 19- 31. |
| 16 | G$\ddot{\rm{o}}$pfert A , Riahi H , Tammer C , et al. Variational Methods in Partially Ordered Spaces[M]. New York: Springer, 2003. |
| 17 | 张石生. 变分不等式及其相关问题[M]. 重庆: 重庆出版社, 2008. |
| 18 | Browder F E . A new generalization of the Schauder fixed point theorem[J]. Annals of Mathematics, 1967, 174, 285- 290. |
| 19 | Aubin J P , Ekeland I . Applied Nonlinear Analysis[M]. New York: John Wiley and Sons, 1984. |
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