Improved Gauss Seidel based projection-contraction algorithm for the mixed complementarity problem in contact problem

The GSCP (Gauss-Seidel based projection-contraction) algorithm has been well established in solving elastoplastic mixed complementarity problems (MiCPs) or other problems which have similar mathematical form. However, the stability problems in the GSPC algorithm may cause nonconvergence or program crashes. Thus, the method of constructing and analyzing counterexamples is adopted to study the reasons for the instability of the GSPC algorithm. The R-GSPC algorithm was developed by modifying the part of the GSPC algorithm that caused the crash to make the algorithm stable. In addition, this paper analyzes the convergence, compatibility, and initial value impact of R-GSPC, and finds that the R-GSPC algorithm greatly improves the robustness and stability without losing accuracy. This paper allows the GSPC algorithm to be better extended to more fields and to be suitabled for being introduced into commercial programs.

Automated summary

The GSCP algorithm has been well established in solving elastoplastic MiCPs or similar problems. However, instability issues in the GSPC algorithm can lead to nonconvergence or program crashes. This paper adopts the method of constructing and analyzing counterexamples to study the instability reasons and develops the stable R-GSPC algorithm by modifying the problematic part. The analysis shows that R-GSPC greatly improves robustness and stability without sacrificing accuracy, making it suitable for commercial programs.