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

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  • Maicon Marques Alves

    (Universidade Federal de Santa Catarina)

  • Samara Costa Lima

    (Universidade Federal de Santa Catarina)

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.

Suggested Citation

  • Maicon Marques Alves & Samara Costa Lima, 2017. "An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 818-847, December.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:3:d:10.1007_s10957-017-1188-y
    DOI: 10.1007/s10957-017-1188-y
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    References listed on IDEAS

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    1. L. C. Ceng & B. S. Mordukhovich & J. C. Yao, 2010. "Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 267-303, August.
    2. Renato D. C. Monteiro & Camilo Ortiz & Benar F. Svaiter, 2016. "An adaptive accelerated first-order method for convex optimization," Computational Optimization and Applications, Springer, vol. 64(1), pages 31-73, May.
    3. M. V. Solodov & B. F. Svaiter, 2000. "An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 214-230, May.
    4. Renato Monteiro & Camilo Ortiz & Benar Svaiter, 2014. "Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems," Computational Optimization and Applications, Springer, vol. 57(1), pages 45-69, January.
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