Scalable Relaxation Two-Sweep Modulus-Based Matrix Splitting Methods for Vertical LCP

Based on a new equivalent reformulation, a scalable modulus-based matrix splitting (SMMS) method is proposed to solve the vertical linear complementarity problem (VLCP). By introducing a relaxation parameter and employing the two-sweep technique, we further enhance the scalability of the method, leading to a framework of the scalable relaxation two-sweep modulus-based matrix splitting (SRTMMS) method. To theoretically demonstrate the acceleration of the convergence provided by the SMMS method, we present a comparison theorem for the case of \(s=2\) $s=2$ . Furthermore, we establish the convergence of the SRTMMS method for arbitrary s. Preliminary numerical results indicate promising performance of the SRTMMS method.