@article{ajmo2013111,
author={{Elfoutayeni, Youssef and Khaladi, Mohamed},
title={General Characterization of a Linear Complementarity Problem},
journal={American Journal of Modeling and Optimization},
volume={1},
number={1},
pages={1--5},
year={2013},
url={http://pubs.sciepub.com/ajmo/1/1/1},
abstract={For a given <img src=image/abs1.png></img> matrix <img src=image/abs2.png></img> and a vector <img src=image/abs3.png></img> of<img src=image/abs4.png></img>, the linear complementarity problem<i> LCP(A,b) </i>is to find a vector <img src=image/abs5.png></img> in <img src=image/abs6.png></img> satisfying<img src=image/abs7.png></img>, <img src=image/abs8.png></img> and <img src=image/abs9.png></img> or showing that such a vector <img src=image/abs10.png></img> does not exist. Under various hypotheses on the matrix<img src=image/abs11.png></img>, <i>LCP</i><i> </i><i>(A,b) </i>was studied by many authors in the last decade. In previous papers we have developed algorithms for solving some classes of <i>LCP</i><i> </i><i>(A,b)</i>. In this work, we give a general characterization of the solutions of <i>LCP</i><i> </i><i>(A,b)</i>, we show under what conditions the problem has a solution or not and how to calculate the solution when they exist. We then apply this characterization to some examples and find the solutions or show that the problem <i>LCP</i><i> </i><i>(A,b)</i> has no solution.},
doi={10.12691/ajmo-1-1-1}
publisher={Science and Education Publishing}
}