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Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces

Lu-Chuan Ceng, Ching-Feng Wen
2012 Journal of Applied Mathematics  
We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach  ...  On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations  ...  Discipline Project of Shanghai Normal University DZL707 and by a grant from the National Science Council of ROC NSC 100-2115-M-037-001 .  ... 
doi:10.1155/2012/194509 fatcat:7a5vprbrungp7lok2ub4pwle3m

Well-posedness by perturbations of variational-hemivariational inequalities with perturbations

Lu-Chuan Ceng, Himanshu Gupta, Ching-Feng Wen
2012 Filomat  
in Banach spaces, which includes as a special case the class of mixed variational inequalities.  ...  Furthermore, in the setting of finite-dimensional spaces we also derive some conditions under which the variational-hemivariational inequality is strongly generalized well-posed-like by perturbations.  ...  [15] generalized the notion of well-posedness by perturbations to a mixed variational inequality in Banach spaces.  ... 
doi:10.2298/fil1205881c fatcat:63evyx7mlrdrbjg7fpbsocf67e

Well-Posedness by Perturbations for Variational-Hemivariational Inequalities

Shu Lv, Yi-bin Xiao, Zhi-bin Liu, Xue-song Li
2012 Journal of Applied Mathematics  
We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities.  ...  We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations  ...  Acknowledgments This work was supposed by the National Natural Science Foundation of China 11101069 and 81171411 , the Fundamental Research Funds for the Central Universities ZYGX2009J100 , and the Open  ... 
doi:10.1155/2012/804032 fatcat:7x5hpbe75jarjcrsb4rl4xgsay

Well-Posedness for a Class of Strongly Mixed Variational-Hemivariational Inequalities with Perturbations

Lu-Chuan Ceng, Ngai-Ching Wong, Jen-Chih Yao
2012 Journal of Applied Mathematics  
The concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations which  ...  is strongly well-posed in the generalized sense.  ...  Recently, Fang, Huang and Yao [10] generalized the concepts of well-posedness and α-well-posedness to a generalized mixed variational inequality which includes as a special case the classical variational  ... 
doi:10.1155/2012/712306 fatcat:cauetwlfk5hmblf4sjhsbm36xi

Theory and Algorithms of Variational Inequality and Equilibrium Problems, and Their Applications

Xie-ping Ding, Nan-jing Huang, Fu-quan Xia, Qing-bang Zhang, Qamrul Hasan Ansari
2014 Abstract and Applied Analysis  
invaluable help in the reviewing process.  ...  Acknowledgments The editors of this special issue would like to express their gratitude to the authors who have submitted their papers for consideration and to the expert referees who provided them with  ...  (II) Well-Posedness and Stability of Equilibrium Problems (i) In the paper titled "Levitin-Polyak well-posedness of an equilibrium-like problem in Banach spaces, " R.  ... 
doi:10.1155/2014/969303 fatcat:3kuuprppaneehnlh25jkxtcpyq

Well-posedness for generalized variational-hemivariational inequalities with perturbations in reflexive banach spaces

Lu-Chuan Ceng, Yung-Yih Lur, Ching-Feng Wen
2017 Tamkang Journal of Mathematics  
In this paper, we consider an extension of well-posedness for a minimization problem to a class of generalized variational-hemivariational inequalities with perturbations in reflexive Banach spaces.  ...  Under some mild conditions, we also prove the equivalence between the α-well-posedness of the generalized variational-hemivariational inequality and the α-well-posedness of the corresponding inclusion  ...  [5, 6] generalized two kinds of well-posedness for a mixed variational inequality problem in Banach space, respectively.  ... 
doi:10.5556/j.tkjm.48.2017.2460 fatcat:kkv2ur7slfg7vhc74f4572bdye

Well-posedness for a class of generalized variational-hemivariational inequalities involving set-valued operators

Caijing Jiang
2018 Journal of Inequalities and Applications  
The aim of present work is to study some kinds of well-posedness for a class of generalized variational-hemivariational inequality problems involving set-valued operators.  ...  Finally, the well-posedness for a class of generalized mixed equilibrium problems is also considered.  ...  Fang [13, 14] generalized two kinds of well-posedness for a mixed variational inequality problem in a Banach space.  ... 
doi:10.1186/s13660-018-1776-x pmid:30137915 pmcid:PMC6061753 fatcat:eeyf7axiy5gkfk3scg3iutir5a

On the Hadamard Well-Posedness of Generalized Mixed Variational Inequalities in Banach Spaces

Lu-Chuan Ceng, Yeong-Cheng Liou, Ching-Feng Wen, Hui-Ying Hu, Long He, Yun-Ling Cui, Yongqiang Fu
2021 Journal of Mathematics  
We introduce a new concept of Hadamard well-posedness of a generalized mixed variational inequality in a Banach space.  ...  The characterizations of Hadamard well-posedness for a generalized mixed variational inequality are established.  ...  In 2013, Li and Xia [12] introduced the concept of Hadamard well-posedness of a general mixed variational inequality in Banach spaces.  ... 
doi:10.1155/2021/9527107 fatcat:x6lndezyhjc77mnoszgz5pqspy

Well-posedness for generalized ( η , g , φ ) $(\eta ,g,\varphi )$ -mixed vector variational-type inequality and optimization problems

Shih-sen Chang, Salahuddin, L. Wang, X. R. Wang, L. C. Zhao
2019 Journal of Inequalities and Applications  
Also we prove that well-posedness of optimization problem is closely related to that of generalized (η, g, ϕ)-mixed vector variational-type inequality problems.  ...  The purpose of this paper is to focus on the well-posedness for a generalized (η, g, ϕ)-mixed vector variational-type inequality and optimization problems with a constraint.  ...  Acknowledgements The authors are very grateful to the referees for their careful reading, comments and suggestions, which improved the presentation of this article.  ... 
doi:10.1186/s13660-019-2194-4 fatcat:wvuf4y6npvaenatzru6umgkh2q

The well-posedness for a system of generalized quasi-variational inclusion problems

Xiao-bo Li, Ravi P Agarwal, Yeol Cho, Nan-jing Huang
2014 Journal of Inequalities and Applications  
Motivated and inspired by research work mentioned above, in this paper, we study the LP and Hadamard well-posedness for the system of generalized quasi-variational inclusion problems.  ...  In Section , we introduce the concept of LP well-posedness for the system of generalized quasi-variational inclusion problems.  ...  . [] introduced the well-posedness by perturbations for variational inequalities and Fang et al. [] considered the well-posedness by perturbations for mixed variational inequalities in Banach spaces  ... 
doi:10.1186/1029-242x-2014-321 fatcat:vnkf6ozuunfgnahhysosjr5pn4

Preface

Marco A. López, Juan Enrique Martínez-Legaz, Alex Shapiro
2009 Mathematical programming  
"Mixed semicontinuous perturbations of nonconvex sweeping processes" (by T. Haddad and L.  ...  "Towards variational analysis in metric spaces: metric regularity and fixed points" (by A.D.  ... 
doi:10.1007/s10107-009-0325-2 fatcat:vniia7lckjaippb2xv45e5f2fq

Page 1193 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Summary: “The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces.  ...  (RS-KAZA-AM; Kazan’); Kum, Sangho Descent methods for mixed variational inequalities in a Hilbert space.  ... 

Well-posedness for systems of time-dependent hemivariational inequalities in Banach spaces

Lu-Chuan Ceng, Yeong-Cheng Liou, Jen-Chih Yao, Yonghong Yao
2017 Journal of Nonlinear Science and its Applications  
In this paper, we generalize the concept of α-well-posedness to a system of time-dependent hemivariational inequalities without Volterra integral terms in Banach spaces.  ...  We establish some metric characterizations of α-well-posedness and prove some equivalence results of strong α-well-posedness (resp., in the generalized sense) between a system of time-dependent hemivariational  ...  In addition, it is well-known that there are many other concepts of well-posedness in the literature on optimization problems and variational inequalities, such as well-posedness by perturbations [2,  ... 
doi:10.22436/jnsa.010.08.26 fatcat:qhplwfsiq5bwfnpvf7itcqfqwq

Well-posedness for bilevel vector equilibrium problems

2019 Applied Set-Valued Analysis and Optimization  
In this paper, we study the well-posedness for bilevel vector equilibrium problems (BVEP) and propose a generalized well-posed concept for the BVEP in Hausdorff topological vector spaces.  ...  Finally, we establish a metric characterization for the generalized wellposedness in terms of the Kuratowski measure of the non-compactness of the approximating solution set.  ...  This paper was supported by the Basic and Advanced Research Project of Chongqing (cstc2016jcyjA0239) and the Graduate Student Innovation Project of Chongqing (CYS18137).  ... 
doi:10.23952/asvao.1.2019.1.03 fatcat:7sg4o237vne2ldbd6ee6e3dldi

On well-posedness associated with a class of controlled variational inequalities

Savin Treanta, Shalini Jha
2021 Mathematical Modelling of Natural Phenomena  
in generalized sense for a class of controlled variational inequality problems.  ...  and well-posedness in generalized sense.  ...  [8] extended this notion of well-posedness by applying perturbations on the mixed variational inequality problem over Banach space and proved various results for well-posedness via perturbations.  ... 
doi:10.1051/mmnp/2021046 fatcat:etmzaqkldrbnhbuen3usgajizu
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