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Inexact proximal stochastic gradient method for convex composite optimization

Author

Listed:
  • Xiao Wang

    (University of Chinese Academy of Sciences)

  • Shuxiong Wang

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

  • Hongchao Zhang

    (Louisiana State University)

Abstract

We study an inexact proximal stochastic gradient (IPSG) method for convex composite optimization, whose objective function is a summation of an average of a large number of smooth convex functions and a convex, but possibly nonsmooth, function. Variance reduction techniques are incorporated in the method to reduce the stochastic gradient variance. The main feature of this IPSG algorithm is to allow solving the proximal subproblems inexactly while still keeping the global convergence with desirable complexity bounds. Different subproblem stopping criteria are proposed. Global convergence and the component gradient complexity bounds are derived for the both cases when the objective function is strongly convex or just generally convex. Preliminary numerical experiment shows the overall efficiency of the IPSG algorithm.

Suggested Citation

  • Xiao Wang & Shuxiong Wang & Hongchao Zhang, 2017. "Inexact proximal stochastic gradient method for convex composite optimization," Computational Optimization and Applications, Springer, vol. 68(3), pages 579-618, December.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:3:d:10.1007_s10589-017-9932-7
    DOI: 10.1007/s10589-017-9932-7
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    References listed on IDEAS

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    1. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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