Asynchronous parallel algorithms for nonconvex optimization

We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a no...

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Veröffentlicht in:Mathematical programming Jg. 184; H. 1-2; S. 121 - 154
Hauptverfasser: Cannelli, Loris, Facchinei, Francisco, Kungurtsev, Vyacheslav, Scutari, Gesualdo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Communication
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Probabilistic models
Theoretical
Variables
Workers
Nonconvex constraints
90C30
65K05
Asynchronous algorithms
68W10
Parallel methods
Probabilistic model
90C26
ISSN:0025-5610, 1436-4646
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Zusammenfassung:We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous implementations in a more faithful way than current state-of-the-art models. Other key features of the framework are: (1) it covers in a unified way several specific solution methods; (2) it accommodates a variety of possible parallel computing architectures; and (3) it can deal with nonconvex constraints. Almost sure convergence to stationary solutions is proved, and theoretical complexity results are provided, showing nearly ideal linear speedup when the number of workers is not too large.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-019-01408-w