J 2019

ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS

CLASON, Christian, Stanislav MAZURENKO and Tuomo VALKONEN

Basic information

Original name

ACCELERATION AND GLOBAL CONVERGENCE OF A FIRST-ORDER PRIMAL-DUAL METHOD FOR NONCONVEX PROBLEMS

Authors

CLASON, Christian (guarantor), Stanislav MAZURENKO (643 Russian Federation, belonging to the institution) and Tuomo VALKONEN

Edition

SIAM JOURNAL ON OPTIMIZATION, PHILADELPHIA, SIAM PUBLICATIONS, 2019, 1052-6234

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10102 Applied mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Impact factor

Impact factor: 2.247

RIV identification code

RIV/00216224:14310/19:00113487

Organization unit

Faculty of Science

DOI

UT WoS

000462593800036

Keywords in English

acceleration; convergence; global; primal-dual; first order; nonconvex

Tags

Změněno: 1/4/2020 22:45, Mgr. Marie Šípková, DiS.

Abstract

V originále

The primal-dual hybrid gradient method, modified (PDHGM, also known as the Chambolle-Pock method), has proved very successful for convex optimization problems involving linear operators arising in image processing and inverse problems. In this paper, we analyze an extension to nonconvex problems that arise if the operator is nonlinear. Based on the idea of testing, we derive new step-length parameter conditions for the convergence in infinite-dimensional Hilbert spaces and provide acceleration rules for suitably (locally and/or partially) monotone problems. Importantly, we prove linear convergence rates as well as global convergence in certain cases. We demonstrate the efficacy of these step-length rules for PDE-constrained optimization problems.