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Modified Partial-Update Newton-Type Algorithms for Unary Optimization

Author

Listed:
  • L. H. Chen

    (City University of Hong Kong)

  • N. Y. Deng

    (The Agricultural University of China)

  • J. Z. Zhang

    (City University of Hong Kong)

Abstract

In this paper, we propose two modified partial-update algorithms for solving unconstrained unary optimization problems based on trust-region stabilization via indefinite dogleg curves. The two algorithms partially update an approximation to the Hessian matrix in each iteration by utilizing a number of times the rank-one updating of the Bunch–Parlett factorization. In contrast with the original algorithms in Ref. 1, the two algorithms not only converge globally, but possess also a locally quadratic or superlinear convergence rate. Furthermore, our numerical experiments show that the new algorithms outperform the trust-region method which uses the partial update criteria suggested in Ref. 1.

Suggested Citation

  • L. H. Chen & N. Y. Deng & J. Z. Zhang, 1998. "Modified Partial-Update Newton-Type Algorithms for Unary Optimization," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 385-406, May.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:2:d:10.1023_a:1022682818387
    DOI: 10.1023/A:1022682818387
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