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A Regularized Gradient Projection Method for the Minimization Problem

Author

Listed:
  • Yonghong Yao
  • Shin Min Kang
  • Wu Jigang
  • Pei-Xia Yang

Abstract

We investigate the following regularized gradient projection algorithm xn+1 = Pc(I − γn(∇f + αnI))xn, n ≥ 0. Under some different control conditions, we prove that this gradient projection algorithm strongly converges to the minimum norm solution of the minimization problem minx∈Cf(x).

Suggested Citation

  • Yonghong Yao & Shin Min Kang & Wu Jigang & Pei-Xia Yang, 2012. "A Regularized Gradient Projection Method for the Minimization Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:259813
    DOI: 10.1155/2012/259813
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    References listed on IDEAS

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    1. Yonghong Yao & Yeol Je Cho & Pei-Xia Yang, 2012. "An Iterative Algorithm for a Hierarchical Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, December.
    2. Yonghong Yao & Yeol Je Cho & Pei-Xia Yang, 2012. "An Iterative Algorithm for a Hierarchical Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Shunhou Fan & Yonghong Yao, 2012. "Strong Convergence of a Projected Gradient Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. M. De la Sen, 2012. "Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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