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.

中文翻译：

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接触问题中混合互补问题的改进的Gauss Seidel投影-收缩算法

GSCP（Gauss-Seidel based projection-contraction）算法在解决弹塑性混合互补问题（MiCPs）或其他具有类似数学形式的问题方面已经得到了很好的建立。但是 GSPC 算法中的稳定性问题可能会导致不收敛或程序崩溃。因此，采用构造反例和分析反例的方法来研究GSPC算法不稳定的原因。R-GSPC算法是通过修改GSPC算法中导致crash的部分，使算法稳定而开发的。此外，本文分析了 R-GSPC 的收敛性、兼容性和初值影响，发现 R-GSPC 算法在不损失准确性的情况下大大提高了鲁棒性和稳定性。