SIAM Journal on Optimization, Volume 30, Issue 1, Page 752-780, January 2020.
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite-dimensional. We consider nonconvex optimization and generalized equations defined on metric spaces and develop bounds on solution errors using the truncated Hausdorff distance applied to graphs and epigraphs of the underlying set-valued mappings and functions. In the process, we extend the calculus of such distances to cover compositions and other constructions that arise in nonconvex problems. The results are applied to constrained problems with feasible sets that might have empty interiors, solution of KKT systems, and optimality conditions for difference-of-convex functions and composite functions.

中文翻译：

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优化和广义方程的稳定性和误差分析

SIAM优化杂志，第30卷，第1期，第752-780页，2020年1月。
对于在解决方案附近缺乏规则性，易受大扰动影响并且可能是无限维的问题，稳定性和错误分析仍然具有挑战性。我们考虑了在度量空间上定义的非凸优化和广义方程，并使用应用于基础集值映射和函数的图和题词的截短Hausdorff距离，开发了解决方案误差的界线。在此过程中，我们将这种距离的演算范围扩展到涵盖非凸问题中出现的成分和其他构造。将结果应用于具有可能的内部空间为空的可行集的约束问题，KKT系统的解以及凸差函数和复合函数的最优条件。