The Exact Modulus of the Generalized Concave Kurdyka-Lojasiewicz Property

• 成果类型: Article; Early Access
• 署名作者: Wang, Xianfu; Wang, Ziyuan
• 署名单位: University of British Columbia
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1227
• 发表日期: 2022
• 关键词: algorithm; nonconvex; minimization

摘要

We introduce a generalized version of the concave Kurdyka-Lojasiewicz (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 BolteSabach-Teboulle proximal alternating linearized minimization algorithm.