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Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization

Author

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  • Gonglin Yuan

    ()

  • Zengxin Wei

    ()

  • Zhongxing Wang

    ()

Abstract

By means of a gradient strategy, the Moreau-Yosida regularization, limited memory BFGS update, and proximal method, we propose a trust-region method for nonsmooth convex minimization. The search direction is the combination of the gradient direction and the trust-region direction. The global convergence of this method is established under suitable conditions. Numerical results show that this method is competitive to other two methods. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Gonglin Yuan & Zengxin Wei & Zhongxing Wang, 2013. "Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 54(1), pages 45-64, January.
  • Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:45-64 DOI: 10.1007/s10589-012-9485-8
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    References listed on IDEAS

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    1. Christian Clason & Karl Kunisch, 2012. "A measure space approach to optimal source placement," Computational Optimization and Applications, Springer, vol. 53(1), pages 155-171, September.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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