The Exact Modulus of the Generalized Concave Kurdyka-Łojasiewicz Property
该文引入广义凹Kurdyka-Łojasiewicz性质，给出其确切模量（即最优凹解奇异化函数），并利用该模量得到Bolte-Sabach-Teboulle近端交替线性化最小化算法迭代总长度的最紧上界。
We introduce a generalized version of the concave Kurdyka-Łojasiewicz (KL) property by employing nonsmooth desingularizing functions. We also present the exact modulus of the generalized concave KL property, which provides an answer to the open question regarding the optimal concave desingularizing function. The exact modulus is designed to be the smallest among all possible concave desingularizing functions. Examples are given to illustrate this pleasant property. In turn, using the exact modulus, we provide the sharpest upper bound for the total length of iterates generated by the celebrated Bolte-Sabach-Teboulle proximal alternating linearized minimization algorithm.