发表机构
Mitsubishi Electric Corporation（三菱电机株式会社）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个度量框架来量化数学规划公式的鲁棒性，并针对LICQ引入逐点半径，推导其显式公式及添加约束的影响。
AI 中文摘要
数学规划公式通常通过代数重构、约束函数的扰动以及约束的添加或移除来进行修改。其中一些修改保持了可行集不变，而另一些则反映了新施加的建模要求，因此改变了优化问题本身。本文开发了一个度量框架，用于量化依赖于公式的性质的鲁棒性。公式被建模为约束函数的类型化集合。在每个固定的类型基数类别内，它们的距离通过最优匹配相同类型的约束并测量在底层函数空间的范数下产生的差异来定义。作为该框架的具体演示，我们研究了线性独立约束资格（LICQ）。我们引入了逐点LICQ半径，定义为从可行公式到在指定点保持可行但在该点不满足LICQ的公式集合的距离。在适当的假设下，我们推导出该半径的显式公式，并刻画了添加单个等式或不等式约束的效果。
英文摘要
Mathematical programming formulations are routinely modified through algebraic reformulations, perturbations of constraint functions, and the addition or removal of constraints. Some of these modifications preserve the feasible set, whereas others reflect newly imposed modeling requirements and therefore change the optimization problem itself. This paper develops a metric framework for quantifying the robustness of formulation-dependent properties. Formulations are modeled as typed collections of constraint functions. Within each fixed typed-cardinality class, their distance is defined by optimally matching constraints of the same type and measuring the resulting discrepancies in a norm on the underlying function space. As a concrete demonstration of the framework, we study the Linear Independence Constraint Qualification (LICQ). We introduce the pointwise LICQ radius, defined as the distance from a feasible formulation to the set of formulations that remain feasible at a prescribed point but fail LICQ there. Under suitable assumptions, we derive an explicit formula for this radius and characterize the effect of adding a single equality or inequality constraint.
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