Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (6): 1144-1152.
Previous Articles Next Articles
Solvability of Directional Perturbed Generalized Mixed Variational Inequalities in Reflexive Banach Spaces
Xueping Luo*(
),Mengtian Cui
- College of Computer Science and Technology, Southwest University for Nationalities, Chengdu 610041
-
Received:2017-10-20Online:2018-12-26Published:2018-12-27 -
Contact:Xueping Luo E-mail:xuepingluo2014@outlook.com -
Supported by:the NSFC(11701480);the Fundamental Research Funds for the Central Universities of Southwest University for Nationalities(2018HQZZ23);the Key Projects of the Education Department of Sichuan Province(18ZA0511);the Innovation Team Funds of Southwest University for Nationalities(14CXTD03);the Innovative Research Team of the Education Department of Sichuan Province(15TD0050);the Sichuan Youth Science and Technology Innovation Research Team(2017TD0028)
CLC Number:
- O177.91
Cite this article
Xueping Luo, Mengtian Cui. Solvability of Directional Perturbed Generalized Mixed Variational Inequalities in Reflexive Banach Spaces[J].Acta mathematica scientia,Series A, 2018, 38(6): 1144-1152.
share this article
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| 1 |
Fan J H , Liu X , Li J L . Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces. Nonlinear Anal TMA, 2009, 70: 3997- 4007
doi: 10.1016/j.na.2008.08.008 |
| 2 |
Xia F Q , Huang N J , Liu Z B . A projected subgradient method for solving generalized mixed variational inequalities. Oper Res Lett, 2008, 36: 637- 642
doi: 10.1016/j.orl.2008.03.007 |
| 3 |
Zhong R Y , Huang N J . Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces. J Optim Theory Appl, 2012, 152: 696- 709
doi: 10.1007/s10957-011-9914-3 |
| 4 |
Zhong R Y , Huang N J . Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces. Numer Alge Control Optim, 2011, 1: 261- 274
doi: 10.3934/naco |
| 5 |
Li X B , Xia F Q . Hadamard well-posedness of a general mixed variational inequality in Banach space. J Glob Optim, 2013, 56: 1617- 1629
doi: 10.1007/s10898-012-9916-1 |
| 6 |
Li X B , Xia F Q . Levitin-Polyak well-posedness of a generalized mixed variational inequality in Banach spaces. Nonlinear Anal TMA, 2012, 75: 2139- 2153
doi: 10.1016/j.na.2011.10.013 |
| 7 |
Daniilidis A , Hadjisavvas N . Coercivity conditions and variational inequalities. Math Program, 1999, 86: 433- 438
doi: 10.1007/s101070050097 |
| 8 | Crouzeix J P . Pseudomonotone variational inequality problems:Existence of solutions. Math Program, 1997, 78: 305- 314 |
| 9 |
Fan J H , Zhong R Y . Stability analysis for variational inequality in reflexive Banach spaces. Nonlinear Anal TMA, 2008, 69: 2566- 2574
doi: 10.1016/j.na.2007.08.031 |
| 10 |
He Y R . Stable pseudomonotone variational inequality in reflexive Banach spaces. J Math Anal Appl, 2007, 330: 352- 363
doi: 10.1016/j.jmaa.2006.07.063 |
| 11 | He Y R . The Tikhonov regularization method for set-valued variational inequalities. Abstr Appl Anal, 2012, Article ID: 172061 |
| 12 | Li F L , He Y R . Solvability of a perturbed variational inequality. Pac J Optim, 2014, 10: 105- 111 |
| 13 |
Aussel D , Hadjisavvas N . On quasimonotone variational inequalities. J Optim Theory Appl, 2004, 121: 445- 450
doi: 10.1023/B:JOTA.0000037413.45495.00 |
| 14 |
Bianchi M , Hadjisavvas N , Schaible S . Exceptional families of elements for variational inequalities in Banach spaces. J Optim Theory Appl, 2006, 129: 23- 31
doi: 10.1007/s10957-006-9041-8 |
| 15 | Facchinei F , Pang J S . Finite-Dimensional Variational Inequalities and Complementarity Problems. New York: Springer-Verlag, 2003 |
| 16 |
Konnov I V . On the convergence of a regularization method for variational inequalities. Comput Math Math Phys, 2006, 46: 541- 547
doi: 10.1134/S0965542506040026 |
| 17 |
Qi H D . Tikhonov regularization methods for variational inequality problems. J Optim Theory Appl, 1999, 102: 193- 201
doi: 10.1023/A:1021802830910 |
| 18 |
Liu J . Sensitivity analysis in nonlinear programs and variational inequalities via continuous selections. SIAM J Control Optim, 1995, 33: 1040- 1060
doi: 10.1137/S0363012993248876 |
| 19 |
Ha C D . Application of degree theory in stability of the complementarity problem. Math Oper Res, 1987, 12: 368- 376
doi: 10.1287/moor.12.2.368 |
| 20 |
Dafermos S . Sensitivity analysis in variational inequalities. Math Oper Res, 1988, 13: 421- 434
doi: 10.1287/moor.13.3.421 |
| 21 |
Kyparisis J . Parametric variational inequalities with multivalued solution sets. Math Oper Res, 1992, 17: 341- 364
doi: 10.1287/moor.17.2.341 |
| 22 |
Qiu Y , Magnanti T L . Sensitivity analysis for variational inequalities. Math Oper Res, 1992, 17: 61- 76
doi: 10.1287/moor.17.1.61 |
| 23 |
Tobin R L . Sensitivity analysis for variational inequalities. J Optim Theory Appl, 1986, 48: 191- 209
doi: 10.1007/BF00938597 |
| 24 |
Gowda M S , Pang J S . Stability analysis of variational inequalities and nonlinear complementarity problems, via the mixed linear complementarity problem and degree theory. Math Oper Res, 1994, 19: 831- 879
doi: 10.1287/moor.19.4.831 |
| 25 |
Zhong R Y , Huang N J . Stability analysis for Minty mixed variational inequality in reflexive Banach spaces. J Optim Theory Appl, 2010, 147: 454- 472
doi: 10.1007/s10957-010-9732-z |
| 26 |
李择均, 孙淑芹. 一个扰动变分不等式的可解性. 数学物理学报, 2016, 36A (3): 473- 480
doi: 10.3969/j.issn.1003-3998.2016.03.009 |
|
Li Z J , Sun S Q . Solvability of a perturbed variational inequality. Acta Math Sci, 2016, 36A (3): 473- 480
doi: 10.3969/j.issn.1003-3998.2016.03.009 |
|
| 27 | Aubin J P . Optima and Equilibria. Berlin: Springer-Verlag, 1993 |
| 28 | Baiocchi C , Buttazzo G , Gastaldi F , Tomarelli F . general existence theorems for unilateral problems in continuum mechanics. Arch Ration Mech Anal, 1998, 100: 149- 188 |
| 29 |
Adly S , Théra M , Ernst E . Stability of the solution set of non-coercive variational inequalities. Commun Contemp Math, 2002, 4: 145- 160
doi: 10.1142/S0219199702000579 |
| 30 |
Fan K . A generalization of Tychonoff's fixed point theorem. Math Ann, 1961, 142: 305- 310
doi: 10.1007/BF01353421 |
| [1] | Li Zejun, Sun Shuqin. Solvability of a Perturbed Variational Inequality [J]. Acta mathematica scientia,Series A, 2016, 36(3): 473-480. |
| [2] | ZHANG Song-Yan, TAO Xiang-Xing. Rough Parametric Marcinkiewicz Integrals on Generalized Campanato Spaces [J]. Acta mathematica scientia,Series A, 2010, 30(1): 154-166. |
|