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Tight Sublinear Convergence Rate of the Proximal Point Algorithm for Maximal Monotone Inclusion Problems

The tight sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems is established based on the squared fixed point residual. By using the performance estimation framework, the tight sublinear convergence rate problem is written as an infinite dimensional nonconvex optimization problem, which is then equivalently reformulated as a finite dimensional semidefinite programming (SDP) problem. By solving the SDP, the exact sublinear rate is computed numerically. Theoretically, by constructing a feasible solution to the dual SDP, an upper bound is obtained for the tight sublinear rate. On the other hand, an example in two dimensional space is constructed to provide a lower bound. The lower bound matches exactly the upper bound obtained from the dual SDP, which also coincides with the numerical rate computed. Hence, we have established the worst case sublinear convergence rate, which is tight in terms of both the order and the constants involved.

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Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.30 No.3 July-September 2020

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 1905 - 1921

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

-

Edisi

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Subjek

SEMIDEFINITE PROGRAMMING
PROXIMAL POINT ALGORITHM
MAXIMAL MONOTONE INCLUSION
TIGHT SUBLINEAR CONVERGENCE RATE
PERFORMANCE ESTIMATION FRAMEWORK

Info Detail Spesifik

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Pernyataan Tanggungjawab

Guoyong Gu, Junfeng Yang

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