线性优化中argmin映射的Hoffman常数
Hoffman constant of the argmin mapping in linear optimization
AI总结：
本文研究线性优化中argmin映射的Hoffman常数，提出了一种基于点的表达式，并引入了well-connected piecewise convex映射的概念，推导了Hoffman常数与 calmness modulus 上确界之间的关键等式。
摘要：
本文的主要目标是为线性优化中argmin映射的Hoffman常数提供一个基于点的表达式，该常数被理解为在其定义域上的sharp Lipschitz常数。本文主要在右端项扰动的约束系统参数上下文中进行研究。据作者所知，这是该常数的第一个精确公式，尽管文献中已有不同的上界估计。本文从更广泛的角度出发，引入了具有自身价值的新工具，如well-connected piecewise convex映射的概念。我们隔离了此类映射的良好行为，以推导Hoffman常数（一种全局稳定性度量）与calmness modulus上确界（局部性质）之间的关键等式。本文还包含关于最优解方向稳定性的一些具体内容，并以结论和关于进一步研究的注记结束。
英文摘要：
The main goal of this paper is to provide a point-based expression for the Hoffman constant of the argmin mapping in linear optimization, understood as the sharp Lipschitz constant restricted to its domain. The work is mainly developed in the parametric context of right-hand side perturbations of the constraint system. To the authors' knowledge, this is the first exact formula for this constant, although we can find in the literature different upper estimates. The paper tackles this objective from a broader perspective, which introduces new tools of their own interest, such as the concept of well-connected piecewise convex mapping. We isolate the nice behavior of such mappings to derive a crucial equality between the Hoffman constant (which is a global stability measure) and the supremum of calmness moduli (of local nature). The paper also includes some specifics about directional stability of optimal solutions and finishes with some conclusions and notes about further research.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
