Mathematics > Optimization and Control
[Submitted on 3 Dec 2018 (v1), last revised 29 Sep 2019 (this version, v3)]
Title:Subregularity of subdifferential mappings relative to the critical set and KL property of exponent 1/2
View PDFAbstract:For a proper extended real-valued function, this work focuses on the relationship between the subregularity of its subdifferential mapping relative to the critical set and its KL property of exponent 1/2. When the function is lsc convex, we establish the equivalence between them under the continuous assumption on the critical set. Then, for the uniformly prox-regular function, under its continuity on the local minimum set, the KL property of exponent 1/2 on the local minimum set is shown to be equivalent to the subregularity of its subdifferential relative to this set. Moreover, for this class of nonconvex functions, under a separation assumption of stationary values, we show that the subregularity of its subdifferential relative to the critical set also implies its KL property of exponent $1/2$. These results provide a bridge for the two kinds of regularity, and their application is illustrated by examples.
Submission history
From: Yulan Liu [view email][v1] Mon, 3 Dec 2018 05:14:16 UTC (17 KB)
[v2] Sat, 8 Dec 2018 02:36:08 UTC (18 KB)
[v3] Sun, 29 Sep 2019 02:29:47 UTC (103 KB)
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