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A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization

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Abstract

By using the Moreau-Yosida regularization and proximal method, a new trust region algorithm is proposed for nonsmooth convex minimization. A cubic subproblem with adaptive parameter is solved at each iteration. The global convergence and Q-superlinear convergence are established under some suitable conditions. The overall iteration bound of the proposed algorithm is discussed. Preliminary numerical experience is reported.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, China

    Sha Lu & Zengxin Wei

  2. School of Mathematical Science, Guangxi Teachers Education University, Nanning, Guangxi, China

    Sha Lu

  3. School of Mathematical Sciences, Guangxi Normal University, Guilin, Guangxi, China

    Lue Li

Authors
  1. Sha Lu
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  2. Zengxin Wei
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  3. Lue Li
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Corresponding author

Correspondence to Sha Lu.

Additional information

This work is supported by the Chinese NSF grants 10761001 and the Scientific Research Foundation of Guangxi University (Grant No. X081082).

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Lu, S., Wei, Z. & Li, L. A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization. Comput Optim Appl 51, 551–573 (2012). https://doi.org/10.1007/s10589-010-9363-1

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  • DOI: https://doi.org/10.1007/s10589-010-9363-1

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