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

• Published in: Journal of optimization theory and applications Vol. 203; no. 1; pp. 714 - 744
• Main Authors: Yu, Dongmei, Wei, Huiling, Chen, Cairong, Han, Deren
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2024; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Artificial intelligence; Calculus of Variations and Optimal Control; Optimization; Convergence; Efficiency; Engineering; Mathematics; Mathematics and Statistics; Methods; Operations Research/Decision Theory; Optimization; Splitting; Theory of Computation; Vertical linear complementarity problem; Two-sweep technique; 90C30; 65F10; Modulus-based matrix splitting method; 65H10; Relaxation technique; Convergence analysis
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-024-02529-9

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 . Furthermore, we establish the convergence of the SRTMMS method for arbitrary s . Preliminary numerical results indicate promising performance of the SRTMMS method.