B-Differentiable Methods For Solving A Class Of Linear Complementarity Problem

In this paper we mainly discussed the B — differentiable methods for solving linear complementarity problems. On the basis of introduction of the research background , meanings and the domestic and abroad study situation, the iterative algorithms are studied mainly from two aspects, local and large-scale convergence. And also we established the corresponding convergence conclusion. Applications of the theory to practical problem were also studied.At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods , and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search.At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings. Numerical results showed that these algorithms were reliable, efficient and are superior to the existing methods.And finally, we put forward some methods and directions for further research methods.