An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization

We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient method, for which pointwise and ergodic iteration-complexity has been established rec...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 175; no. 3; pp. 818 - 847
Main Authors: Alves, Maicon Marques, Lima, Samara Costa
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2017
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Complexity
Computational geometry
Convexity
Engineering
Inverse method
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Splitting
Theory of Computation
Iteration-complexity
Splitting
47J20
Partial inverse method
90C33
Composite optimization
Forward–backward
90C060
65K10
Inexact proximal point methods
Parallel
47H05
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient method, for which pointwise and ergodic iteration-complexity has been established recently by Monteiro and Svaiter. As applications, we propose and analyze the iteration-complexity of an inexact operator splitting algorithm—which generalizes the original Spingarn’s splitting method—and of a parallel forward–backward algorithm for multi-term composite convex optimization.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-017-1188-y