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Adaptive Douglas-Rachford Splitting Algorithm from a Yosida Approximation Standpoint

The adaptive Douglas--Rachford splitting algorithm iteratively applies the operator T=κnQAQB+(1−κn)Id to solve the inclusion problem zer(A+B). By taking a Yosida approximation standpoint, we express in canonical form QAQB=(Id−(γ+λ) γA)∘(Id−(γ+λ) λB). We extend the domain of indices γ,λ to the entire real line, so that the adaptive algorithm is able to encompass a forward-backward splitting algorithm into one unified framework. Convergence results for both primal and dual problems are proved for different combinations of (strongly and weakly) monotone and comonotone operators. Under the “monotone + comonotone” assumption, we obtain a better rate bound for linear convergence than the classical Douglas--Rachford algorithm.

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Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.31 No.3 July-September 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1971-1998

Bahasa

English

ISBN/ISSN

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Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

FORWARD-BACKWARD ALGORITHM
RESOLVENT
INCLUSION PROBLEM
LINEAR CONVERGENCE
WEAK MONOTONICITY
ADAPTIVE DOUGLAS--RACHFORD ALGORITHM
YOSIDA APPROXIMATION
COMONOTONE

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Pernyataan Tanggungjawab

Zihan Liu, Kannan Ramchandran

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