An Interval Matrix Based Generalized Newton Method for Linear Complementarity Problems

Abstract

The penalty equation of LCP is transformed into the absolute value equation, and then the existence of solutions for the penalty equation is proved by the regularity of the interval matrix. We propose a generalized Newton method for solving the linear complementarity problem with the regular interval matrix based on the nonlinear penalized equation. Further, we prove that this method is convergent. Numerical experiments are presented to show that the generalized Newton method is effective.

A Singular Values Based Newton Method for Linear Complementarity Problems

“…In this section, we will propose that a new generalized Newton method based on the nonlinear penalized Equation (1.2) for solving the linear complementarity problem. Proposition 1 [15].…”

“…In this section, we give some numerical results in order to show the practical performance of Algorithm 2. [16], Jiang and Qi [17], YONG Long-quan, DENG Fang-an, CHEN Tao [18] and Han [15]): 1,1, 1,1, 1,1…”