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

Maicon Marques Alves () and Samara Costa Lima ()
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Maicon Marques Alves: Universidade Federal de Santa Catarina
Samara Costa Lima: Universidade Federal de Santa Catarina

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 3, No 10, 818-847

Abstract: Abstract 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.

Keywords: Inexact proximal point methods; Partial inverse method; Splitting; Composite optimization; Forward–backward; Parallel; Iteration-complexity; 47H05; 47J20; 90C060; 90C33; 65K10 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1188-y

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