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Volume 4, Issue 2 (2014), Pages [59] - [91]
PROJECTIVE ITERATIVE METHODS FOR SOLVING LINEAR COMPLEMENTARITY PROBLEMS: A SURVEY
[1] K. G. Murty, Linear Complementarity, Linear and Nonlinear Programming, Heldermann Verlag,
[2] M. S. Bazaraa, H. D. Sheral and C. M. Shetty, Nonlinear Programming, Theory and Algorithms, Third Edition, Wiley-Interscience,
[3] R. W. Cottle, J. S. Pang and R. E. Stone, The Linear Complementarity Problem, Academic Press, London, 1992.
[4] C. Hildereth, Point estimates of ordinates of concave function, Journal of the American Statistical Association 49 (1954), 598-619.
[5] D. G. Christopherson, A new mathematical method for the solution of film lubrication problems,
[6] C. W. Cryer, The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences, Mathematics of Computation 25 (1971), 435-443.
[7] C. W. Cryer, The solution of a quadratic programming problem using systematic overrelaxation, SIAM J. Control 9 (1971), 385-392.
[8] A. A. Rainondi and J. Boyd, A solution for the finite journal bearing and its application to analysis and design, III, Transactions of the American Society of Lubrication Engineers 1 (1958), 194-209.
[9] V. M. Friedman and V. S. Chernina, An iteration process for the solution of the finite dimensional contact problem, USSR Computational Mathematics and Mathematical Physics 8 (1967), 210-214.
[10] Z. Z. Bai and D. J. Evans, Matrix multisplitting relaxation methods for linear complementarity problems, Int. J. Comput. Math. 63 (1997), 309-326.
[11] D. Yuan and Y. Z. Song, Modified AOR methods for linear complementarity problem, Appl. Math. Comput. 140 (2003), 53-67.
[12] Lj. Cvetković and S. Rapajić, How to improve MAOR method convergence area for linear complementarity problems, Appl. Math. Comput. 162 (2005), 577-584.
[13] Y. Li and P. Dai, Generalized AOR methods for linear complementarity problem, Appl. Math. Comput. 188 (2007), 7-18.
[14] M. H. Xu and G. F. Luan, A rapid algorithm for a class of linear complementarity problems, Appl. Math. Comput. 188 (2007), 1647-1655.
[15] M. Dehghan and M. Hajarian, Convergence of SSOR methods for linear complementarity problems, Operations Research Letters 37 (2009), 219-223.
[16] Z. Z. Bai, Modulus-based matrix splitting iteration methods for linear complementarity problems, Numer. Linear Algebra Appl. 17 (2010), 917-933.
[17] X. Han, D. Yuan and D. S. Jiang, Two SAOR iterative formats for solving linear complementarity problems, Int. J. Information Technology and Computer Science 2 (2011), 38-45.
[18] H. Saberi Najafi and S. A. Edalatpanah, On the two SAOR iterative formats for solving linear complementarity problems, Int. J. Information Technology and Computer Science 3(5) (2011), 19-24.
[19] H. Saberi Najafi and S. A. Edalatpanah, A kind of symmetrical iterative methods to solve special class of LCP (M, q), International Journal of Applied Mathematics and Applications 4(2) (2012), 183-189.
[20] H. Saberi Najafi and S. A. Edalatpanah, On the convergence regions of generalized AOR methods for linear complementarity problems, Journal of Optimization Theory and Applications 156 (2013), 859-866.
[21] H. Saberi Najafi and S. A. Edalatpanah, Iterative methods with analytical preconditioning technique to linear complementarity problems: Application to obstacle problems, RAIRO-Operations Research 47 (2013), 59-71.
doi:10.1051/ro/2013027.
[22] H. Saberi Najafi and S. A. Edalatpanah, SOR-like methods for non-Hermitian positive definite linear complementarity problems, Advanced Modeling and Optimization 15 (2013), 697-704.
[23] H. Saberi Najafi and S. A. Edalatpanah, Modification of iterative methods for solving linear complementarity problems, Engineering Computations 30(7) (2013), 910-923.
[24] R. S. Varga, Matrix Iterative Analysis, Second Edition, Springer,
[25] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press,
[26] O. L. Mangasarian and R. De Leone, Parallel successive overrelaxation methods for symmetric linear complementarity problems and linear programs, J. Optim. Theory Appl. 54 (1987), 437-446.
[27] R. De Leone and O. L. Mangasarian, Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem, Math. Programming 42 (1988), 347-361.
[28] Z. Z. Bai and D. J. Evans, Matrix multisplitting methods with applications to linear complementarity problems: Parallel asynchronous methods, Int. J. Comput. Math. 79 (2002), 205-232.
[29] A. Hadjidimos, Accelerated overrelaxation method, Math. Comput. 32 (1978), 149-157.
[30] D. J. Evans and M. M. Martins, On the convergence of the extrapolated AOR method, Int. J. Comput. Math. 43 (1992), 161-171.
[31] B. Truyen and J. Cornelis, Adiabatic layering: A new concept of hierarchical multi-scale optimization, Neural Networks 8 (1995), 1373-1378.
[32] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA, 1994.
[33] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland Publishing Company,
[34] N. Machida, M. Fukushima and T. Ibaraki, A multisplitting method for symmetric linear complementarity problems, J. Comput. Appl. Math. 62 (1995), 217-227.
[35] Z. Z. Bai, The convergence of parallel iteration algorithms for linear complementarity problems, Comput. Math. Appl. 32 (1996), 1-17.
[36] Z. Z. Bai, On the convergence of the multisplitting methods for the linear complementarity problem, SIAM J. Matrix Anal. Appl. 21 (1999), 67-78.