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The Exact Modulus of the Generalized Concave Kurdyka-Łojasiewicz Property

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.

Ketersediaan

Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.47 No.4 November 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2765-2783

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

NONCONVEX OPTIMIZATION
KURDYKA-LOJASIEWICZ PROPERTY
GENERALIZED CONCAVE KURDYKA-LOJADIEWICZ PROPERTY
OPTIMAL CONCAVE DESINGULARIZING FUNCTION
BOLTE-DANILIDIS-LEY-MAZET DESINGULARIZING FUNCTION
PROXIMAL ALTERNATING LINEARIZED MINIMIZATION

Info Detail Spesifik

https://doi.org/10.1287/moor.2021.1227

Pernyataan Tanggungjawab

Xianfu Wang, Ziyuan Wang

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