自反巴拿赫空间中方向扰动的广义混合变分不等式的可解性

Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (6): 1144-1152.

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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:2017-10-20 Online:2018-12-26 Published: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)

Abstract

Abstract:

Solvability of directional perturbed generalized mixed variational inequalities is discussed in reflexive Banach spaces, under a coercivity condition. In particular, the result we present that the set is directional perturbed is new. Our results generalize and extend some known results in this area (Acta Math Sci, 2016, 36A(3):473-480).

Key words: Generalized mixed variational inequality, Existence and boundedness, Directional perturbation, Coercivity condition

CLC Number:

O177.91

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.

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References

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
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
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
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
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
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
7	Daniilidis A , Hadjisavvas N . Coercivity conditions and variational inequalities. Math Program, 1999, 86: 433- 438
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
10	He Y R . Stable pseudomonotone variational inequality in reflexive Banach spaces. J Math Anal Appl, 2007, 330: 352- 363
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
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
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
17	Qi H D . Tikhonov regularization methods for variational inequality problems. J Optim Theory Appl, 1999, 102: 193- 201
18	Liu J . Sensitivity analysis in nonlinear programs and variational inequalities via continuous selections. SIAM J Control Optim, 1995, 33: 1040- 1060
19	Ha C D . Application of degree theory in stability of the complementarity problem. Math Oper Res, 1987, 12: 368- 376
20	Dafermos S . Sensitivity analysis in variational inequalities. Math Oper Res, 1988, 13: 421- 434
21	Kyparisis J . Parametric variational inequalities with multivalued solution sets. Math Oper Res, 1992, 17: 341- 364
22	Qiu Y , Magnanti T L . Sensitivity analysis for variational inequalities. Math Oper Res, 1992, 17: 61- 76
23	Tobin R L . Sensitivity analysis for variational inequalities. J Optim Theory Appl, 1986, 48: 191- 209
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
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
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
26	Li Z J , Sun S Q . Solvability of a perturbed variational inequality. Acta Math Sci, 2016, 36A (3): 473- 480
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
30	Fan K . A generalization of Tychonoff's fixed point theorem. Math Ann, 1961, 142: 305- 310

[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.

Solvability of Directional Perturbed Generalized Mixed Variational Inequalities in Reflexive Banach Spaces

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