Application of penalty methods to generalized variational inequalities in Banach spaces


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


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