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Scaled Diagonal Gradient‐Type Method with Extra Update for Large‐Scale Unconstrained Optimization

Author

Listed:
  • Mahboubeh Farid
  • Wah June Leong
  • Najmeh Malekmohammadi
  • Mustafa Mamat

Abstract

We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant.

Suggested Citation

  • Mahboubeh Farid & Wah June Leong & Najmeh Malekmohammadi & Mustafa Mamat, 2013. "Scaled Diagonal Gradient‐Type Method with Extra Update for Large‐Scale Unconstrained Optimization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:532041
    DOI: 10.1155/2013/532041
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    References listed on IDEAS

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    1. Mahboubeh Farid & Wah June Leong & Lihong Zheng, 2012. "Accumulative Approach in Multistep Diagonal Gradient‐Type Method for Large‐Scale Unconstrained Optimization," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Mahboubeh Farid & Wah June Leong & Lihong Zheng, 2012. "Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, July.
    3. M. Al-Baali, 1998. "Numerical Experience with a Class of Self-Scaling Quasi-Newton Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 533-553, March.
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