1. Using vector divisions in solving the linear complementarity problem
- Author
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Elfoutayeni, Youssef and Khaladi, Mohamed
- Subjects
- *
VECTOR analysis , *LINEAR complementarity problem , *PROBLEM solving , *NONLINEAR systems , *APPROXIMATION theory , *NUMERICAL analysis , *ALGORITHMS - Abstract
Abstract: The linear complementarity problem is to find a vector in satisfying , ,, where and are given. In this paper, we use the fact that solving is equivalent to solving the nonlinear equation where is a function from into itself defined by . We build a sequence of smooth functions which is uniformly convergent to the function . We show that, an approximation of the solution of the (when it exists) is obtained by solving for a parameter large enough. Then we give a globally convergent hybrid algorithm which is based on vector divisions and the secant method for solving . We close our paper with some numerical simulations to illustrate our theoretical results, and to show that this method can solve efficiently large-scale linear complementarity problems. [Copyright &y& Elsevier]
- Published
- 2012
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