Informace o publikaci

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

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CLASON Christian MAZURENKO Stanislav VALKONEN Tuomo

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj SIAM JOURNAL ON OPTIMIZATION
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://epubs.siam.org/doi/10.1137/18M1170194
Doi http://dx.doi.org/10.1137/18M1170194
Klíčová slova acceleration; convergence; global; primal-dual; first order; nonconvex
Popis 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.

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