General Characterization of a Linear Complementarity Problem
Youssef Elfoutayeni, Mohamed Khaladi · American Journal of Modeling and Optimization · 2013
For a given matrix and a vector of, the linear complementarity problem LCP(A,b) is to find a vector in satisfying, and or showing that such a vector does not exist. Under various hypotheses on the matrix, LCP (A,b) was studied by many authors in the last decade. In previous papers we have developed algorithms for solving some classes of LCP (A,b). In this work, we give a general characterization of the solutions of LCP (A,b), 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 LCP (A,b) has no solution.