The Linear Complementarity Problem and a Method to Find all its Solutions

To solve a linear complementarity problem LCP, almost all the authors assume that this problem admits one and only one solution, and they give a method to calculate this solution. The aim of this paper is to solve LCP when this problem has several solutions.

[1]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[2]  Phillipp Kaestner,et al.  Linear And Nonlinear Programming , 2016 .

[3]  J. Pang.  Necessary and sufficient conditions for the convergence of iterative methods for the linear complementarity problem , 1984 .

[4]  Hao Liu,et al.  A modified general modulus-based matrix splitting method for linear complementarity problems of H-matrices , 2014 .

[5]  Ning Zheng,et al.  Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an H+-matrix , 2014, J. Comput. Appl. Math..

[6]  S. J. Chung.  NP-Completeness of the linear complementarity problem , 1989 .

[7]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[8]  Changfeng Ma,et al.  On the convergence analysis of two-step modulus-based matrix splitting iteration method for linear complementarity problems , 2014, Appl. Math. Comput..

[9]  Li-Tao Zhang,et al.  The weaker convergence of modulus-based synchronous multisplitting multi-parameters methods for linear complementarity problems , 2014, Comput. Math. Appl..

[10]  David J. Evans,et al.  Matrix multisplitting relaxation methods for linear complementarity problems , 1997, Int. J. Comput. Math..

[11]  Masao Fukushima,et al.  A multisplitting method for symmetric linear complementarity problems , 1995 .

[12]  Yaotang Li,et al.  Generalized AOR methods for linear complementarity problem , 2007, Appl. Math. Comput..

[13]  M. Khaladi,et al.  A New Interior Point Method for Linear Complementarity Problem , 2010 .

[14]  Katta G. Murty,et al.  Linear complementarity, linear and nonlinear programming , 1988 .

[15]  Youssef Elfoutayeni,et al.  Using vector divisions in solving the linear complementarity problem , 2012, J. Comput. Appl. Math..

[16]  Xiangke Liao,et al.  IGAOR and multisplitting IGAOR methods for linear complementarity problems , 2011, J. Comput. Appl. Math..

[17]  M. Khaladi,et al.  A Min-Max Algorithm for Solving the Linear Complementarity Problem , 2013 .

[18]  O. Mangasarian.  Solution of symmetric linear complementarity problems by iterative methods , 1977 .