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

Dongmei Yu (), Huiling Wei (), Cairong Chen () and Deren Han ()
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Dongmei Yu: Liaoning Technical University
Huiling Wei: Liaoning Technical University
Cairong Chen: Fujian Normal University
Deren Han: Beihang University

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 26, 714-744

Abstract: Abstract 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.

Keywords: Vertical linear complementarity problem; Modulus-based matrix splitting method; Two-sweep technique; Relaxation technique; Convergence analysis; 65F10; 65H10; 90C30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02529-9

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