Modified Partial-Update Newton-Type Algorithms for Unary Optimization

L. H. Chen, N. Y. Deng and J. Z. Zhang
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L. H. Chen: City University of Hong Kong
N. Y. Deng: The Agricultural University of China
J. Z. Zhang: City University of Hong Kong

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 2, No 7, 385-406

Abstract: 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.

Keywords: Unary optimization; trust-region methods; indefinite dogleg curve; Bunch–Parlett factorization; rank-one update (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022682818387

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