How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?
研究了绝对光滑优化问题中线性独立扭结资格条件（LIKQ）的严格性，利用微分拓扑工具证明该条件在可行点处是通用的，从而支持多项式时间可检验的最优性条件推导。
Abstract Abs-smooth functions are given by compositions of smooth functions and the evaluation of the absolute value. The linear independence kink qualification (LIKQ) is a fundamental assumption in optimization problems governed by these abs-smooth functions, generalizing the well-known LICQ from smooth optimization. In particular, provided that LIKQ holds it is possible to derive optimality conditions for abs-smooth optimization problems that can be checked in polynomial time. Utilizing tools from differential topology, namely a version of the jet-transversality theorem, it is shown that assuming LIKQ for all feasible points of an abs-smooth optimization problem is a generic assumption.