Application of penalty methods to generalized variational inequalities in Banach spaces
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Authors
G. W. Su
- Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, College of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, P. R. China.
Z. W. Zhao
- Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, P. R. China.
Abstract
In this paper, we consider a class of generalized variational
inequalities (GVI) in infinite dimensional Banach spaces, in which
only approximation sequences for GVI are known instead of exact
values of the cost mapping and feasible set. A sequence of inexact
solutions of auxiliary problems involving general penalty method is
introduced. We obtain some convergence properties of the perturbed
version of the regularized penalty method under mild coercive
conditions, which extend some well-known results of variational
inequalities in many respects.
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ISRP Style
G. W. Su, Z. W. Zhao, Application of penalty methods to generalized variational inequalities in Banach spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5311--5320
AMA Style
Su G. W., Zhao Z. W., Application of penalty methods to generalized variational inequalities in Banach spaces. J. Nonlinear Sci. Appl. (2017); 10(10):5311--5320
Chicago/Turabian Style
Su, G. W., Zhao, Z. W.. "Application of penalty methods to generalized variational inequalities in Banach spaces." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5311--5320
Keywords
- Generalized variational inequality
- penalty method
- regularization
- coercivity conditions
- equilibrium problem
MSC
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