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Inertial Proximal Block Coordinate Method for a Class of Nonsmooth Sum-of-Ratios Optimization Problems

In this paper, we consider a class of nonsmooth sum-of-ratios fractional optimization problems with block structure. This model class is ubiquitous and encompasses several important nonsmooth optimization problems in the literature. We first propose an inertial proximal block coordinate method for solving this class of problems by exploiting the underlying structure. The global convergence of our method is guaranteed under the Kurdyka–Łojasiewicz (KL) property and some mild assumptions. We then identify the explicit exponents of the KL property for three important structured fractional optimization problems. In particular, for the sparse generalized eigenvalue problem with either cardinality regularization or sparsity constraint, we show that the KL exponents are 1/2, and so the proposed method exhibits a linear convergence rate. Finally, we illustrate our theoretical results with both analytic and simulated numerical examples.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.33 No.2 April-June 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 361-393

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

SPARSITY
LINEAR CONVERGENCE
FRACTIONAL PROGRAM
PROXIMAL BLOCK COORDINATE METHOD
SUM-OF-RATIOS

Info Detail Spesifik

https://doi.org/10.1137/22M1472000

Pernyataan Tanggungjawab

Radu Ioan Bot, Minh N. Dao, Guoyin Li

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