We present conditions for Hölder calmness and upper Hölder continuity of optimal solution sets to perturbed optimization problems in finite dimensions. Studies on Hölder type stability were a popular subject in variational analysis already in the 1980s and 1990s, and have become a revived interest in the last decade. In this paper, we focus on conditions for Hölder calmness of the argmin mapping in the case of non-isolated minima. We recall known ideas and results in this context for general as well as special parametric programs, refine them and discuss particular settings, including nonlinear programs and convex semi-infinite optimization problems.

我们提出了最优解集的 Hölder 平静性和上 Hölder 连续性条件，以解决有限维中的扰动优化问题。Hölder 型稳定性研究在 1980 年代和 1990 年代已经成为变分分析中的热门课题，并在过去十年中重新引起人们的兴趣。在本文中，我们关注非孤立最小值情况下 argmin 映射的 Hölder 平静条件。我们在此背景下针对一般和特殊参数程序回顾已知的想法和结果，对其进行改进并讨论特定设置，包括非线性程序和凸半无限优化问题。