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A new alternating direction method for co-coercive variational inequality problems

Wenxing Zhang, Deren Han
2009 Computers and Mathematics with Applications  
This paper presents a new alternating direction method for solving co-coercive variational inequality problems, where the feasible set is the intersection of a simple set and polyhedron defined by a system  ...  Lo, A new alternating direction method for a class of nonlinear variational inequality problems, Journal of Optimization Theory and Applications 112 (3) (2002) 549-560] for such class of variational inequality  ...  Conclusions In this paper, we propose a new alternating method to solve variational inequality problems with co-coercive mappings and the feasible set is the intersection of a simple set with a hyperplane  ... 
doi:10.1016/j.camwa.2008.09.049 fatcat:ahsb4rexijdw7d34lgdts3u7be

An iterative method for general mixed variational inequalities

M.A. Noor
2000 Computers and Mathematics with Applications  
As special cases, we obtain various known and new results for solving various classes of variational inequalities and related problems. (~)  ...  An iterative method for solving general mixed variational inequalities is suggested by using the auxiliary principle technique.  ...  These alternative formulations have been used to develop a number of iterative type methods for solving mixed variational inequalities.  ... 
doi:10.1016/s0898-1221(00)00151-6 fatcat:hi2rksignvhrnkizmjcncyll5y

A New Type Method for the Structured Variational Inequalities Problem

Chengjiang Yin
2013 International Journal of Advanced Computer Science and Applications  
In this paper, we present an algorithm for solving the structured variational inequality problem, and prove the global convergence of the new method without carrying out any line search technique, and  ...  ACKNOWLEDGMENT The author wish to give their sincere thanks to the editor and the anonymous referees for their valuable suggestions and helpful comments which improved the presentation of the paper.  ...  Han ([8] ) proposed a modified alternating direction method for variational inequalities with linear constraints.  ... 
doi:10.14569/ijacsa.2013.040323 fatcat:bdfvlv4nv5clxim6b5aj6ps7bu

A new alternating direction method for solving variational inequalities

Abdellah Bnouhachem, M.H. Xu, Mohamed Khalfaoui, Sheng Zhaohan
2011 Computers and Mathematics with Applications  
We introduce a modified alternating direction method for structured monotone variational inequalities by performing an additional projection step at each iteration and another optimal step length is employed  ...  This method only needs functional values for given variables in the solution process and avoids the task of estimating the co-coercive modulus.  ...  Acknowledgments This research was supported partly by NSFC Grants Nos: 70731002 and 70571034, ''The Second Term '985' Engineering-Innovation Center for Computational Laboratory of Evolutionary Economic  ... 
doi:10.1016/j.camwa.2011.05.043 fatcat:wrheqa3zyzh3vdfmhktawgim4q

Page 6255 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
A global convergence theorem is es- tablished for a monotone variational inequality problem without the requirement of co-coercivity of the mapping.  ...  |Han, Deren] (PRC-NAN; Nanjing) A modified alternating direction method for variational inequality problems. (English summary) Appl. Math. Optim. 45 (2002), no. 1, 63-74.  ... 

Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming

Paul Tseng
1990 Mathematical programming  
A classical method for solving the variational inequality problem is the projection algorithm.  ...  Moreover, we extend the projection algorithm to solve any monotone affine variational inequality problem.  ...  'A number of new decomposition algorithms for solving variational inequality problems and convex programs can also be derived from it [Gab83] , [Tse88] .  ... 
doi:10.1007/bf01582258 fatcat:epco4refircxjmbklcliq3ellm

Page 3191 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
variational inequalities by a new alternating direction method.  ...  In this paper, we propose a new alternating direction method for solving a class of monotone variational inequalities.  ... 

Unification of distance inequalities for linear variational problems

José Alberto Cuminato, Vitoriano Ruas
2014 Computational and Applied Mathematics  
More particularly such an approach gives rise to both an improvement and a generalization to the weakly coercive case, of second Strang's inequality for abstract coercive problems.  ...  This is done in a general hilbertian framework, and in this sense, well-known inequalities such as Céa's or Babuška's for coercive and non coercive problems are extended and/or refined, as mere by-products  ...  The authors would like to thank their colleague Gustavo Buscaglia for helpful comments.  ... 
doi:10.1007/s40314-014-0163-6 fatcat:j2q5ozh65fculjoi276xawaxfq

Existence results for quasi variational inequalities

Muhammad Aslam Noor
2007 Banach Journal of Mathematical Analysis  
We this equivalent alternative formulation to discuss the existence of a solution of quasi variational inequalities under some mild conditions.  ...  Since the quasi variational inequalities include variational inequalities, implicit complementarity problems and optimization problems as special cases, results proved in this paper continue to hold these  ...  These activities have motivated to generalize and extend the variational inequalities and related optimization problems in several directions using new and novel techniques.  ... 
doi:10.15352/bjma/1240336215 fatcat:u7hlmz3konhmpiyykir2xlcyzi

On the Finite Element Solution of the Pure Neumann Problem

Pavel Bochev, R. B. Lehoucq
2005 SIAM Review  
Our goal is to present a concise variational framework for the finite element solution of the Neumann problem that focuses on the interplay between the algebraic and variational problems.  ...  Our paper contributes a simple, yet insightful link between the continuous and algebraic variational forms that will prove useful.  ...  We would like to thank Doug Arnold, Martin Berggren, Quang Du and Axel Klawonn for helpful discussions and Ulrich Hetmaniuk for generating Matlab code for the matrices and source terms used in the experiments  ... 
doi:10.1137/s0036144503426074 fatcat:wbxrag24qbcntlzjyaemfpe6fa

A Descent-Projection Method For Solving Monotone Structured Variational Inequalities

Min Sun, Zhenyu Liu
2011 Zenodo  
In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed.  ...  Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.  ...  Recently, for co-coercive variational inequalities, Yan, Han and Sun [9] proposed a self-adaptive projection method which direction d(u k , β k ) and step-size ρ(u k , β k ) don't converge to zero.  ... 
doi:10.5281/zenodo.1332996 fatcat:difk3iy6enelfgpsmfdthuwngm

Formulation of the tangential velocity slip problem in terms of variational inequalities

Antonio Strozzi, Matteo Giacopini, Enrico Bertocchi, Daniele Dini
2014 Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology  
For instance, variational inequalities have been used in the description of the cavitation problem.  ...  modelling of the tangential velocity slip problem in terms of variational inequalities.  ... 
doi:10.1177/1350650114530680 fatcat:w5erhbhpobbptp7w2ag24iljci

Is the Helmholtz Equation Really Sign-Indefinite?

Andrea Moiola, Euan A. Spence
2014 SIAM Review  
of the Laplacian), and thus the variational problem cannot be sign-definite.  ...  In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions  ...  Acknowledgements The authors thank the following for useful comments and discussions: Xavier Antoine  ... 
doi:10.1137/120901301 fatcat:u477ej5uyjakve2ktvqwsa3s7y

Variational inequalities and free boundary problems

David Kinderlehrer
1978 Bulletin of the American Mathematical Society  
A general introduction to variational inequalities is provided in the papers [Li-S], [L-Sl], and [Brl].  ...  The study of variational inequalities and free boundary problems finds application in a variety of disciplines including physics, engineering, and economics as well as potential theory and geometry.  ...  The method of penalization consists in replacing the variational inequality (1.5) by a family of nonlinear boundary value problems resembling (2.1) and then demonstrating that their solutions converge  ... 
doi:10.1090/s0002-9904-1978-14397-3 fatcat:cko6vtigjndmbh2gkorwglpghi

Generalized projection theorem with application to linear noncoercive equations and some nonlinear situations

Tapas Mazumdar
1973 Journal of Mathematical Analysis and Applications  
In Section 5, we will have one more occasion to refer to variational inequalities.  ...  Noncoercive situations arise also in [5] in connection with elliptic operators and in [21, p. 381 in connection with variational inequalities.  ...  In accordance with the spirit of [21, p. 151, we will not dwell on whether this inequality corresponds to a problem in the calculus of variations-it may well not.  ... 
doi:10.1016/0022-247x(73)90258-8 fatcat:cdbwoqqy25ff3nil4n6pra5tsy
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