Generalized Modulus-Based Iterative Method with Acceleration Parameter for Large-Scale Sparse Linear Complementarity Problems

A family of generalized modulus-based iterative schemes incorporating an acceleration mechanism is proposed for large-scale sparse linear complementarity problems. The proposed approach is based on a generalized matrix splitting strategy involving an acceleration parameter, which extends several existing accelerated modulus-based methods as special cases. Convergence of the proposed schemes is guaranteed under certain conditions when the coefficient matrix belongs to the class of $P$-matrices or $H_{+}$-matrices, and several numerical experiments are included to illustrate their computational performance. The numerical results show that the generalized accelerated methods significantly reduce the number of iterations and CPU time compared with existing approaches, thereby improving convergence performance for large-scale sparse problems.