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Modified Partial-Update Newton-Type Algorithms for Unary Optimization

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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.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Hong Kong

    L. H. Chen (PhD Student)

  2. Division of Basic Science, The Agricultural University of China, China

    N. Y. Deng (Professor)

  3. Department of Mathematics, City University of Hong Kong, Hong Kong

    J. Z. Zhang (Associate Professor)

Authors
  1. L. H. Chen
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  2. N. Y. Deng
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  3. J. Z. Zhang
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Chen, L.H., Deng, N.Y. & Zhang, J.Z. Modified Partial-Update Newton-Type Algorithms for Unary Optimization. Journal of Optimization Theory and Applications 97, 385–406 (1998). https://doi.org/10.1023/A:1022682818387

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  • DOI: https://doi.org/10.1023/A:1022682818387

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