Convergence analysis on matrix splitting iteration algorithm for semidefinite linear complementarity problems

In this paper, we present some novel observations for the semidefinite linear complementarity problems, abbreviated as SDLCPs. Based on these new results, we establish the modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently SDLCP as an implicit fixed-point matrix equation. The convergence of the proposed modulus-based matrix splitting iteration methods has been analyzed. Numerical experiments have shown that the modulus-based iteration methods are effective for solving SDLCPs.

Automated summary

Novel observations for SDLCPs are presented in this paper, leading to the establishment of modulus-based matrix splitting iteration methods. The convergence of these methods has been analyzed and numerical experiments have shown their effectiveness in solving SDLCPs.