Superlinearly Convergent Trust-Region Method without the Assumption of Positive-Definite Hessian

J. L. Zhang, Y. Wang and X. S. Zhang
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J. L. Zhang: Management School of Graduate University, Chinese Academy of Sciences
Y. Wang: Academy of Mathematics and Systems Science, Chinese Academy of Sciences
X. S. Zhang: Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Journal of Optimization Theory and Applications, 2006, vol. 129, issue 1, No 12, 218 pages

Abstract: Abstract In this paper, we reinvestigate the trust-region method by reformulating its subproblem: the trust-region radius is guided by gradient information at the current iteration and is self-adaptively adjusted. A trust-region algorithm based on the proposed subproblem is proved to be globally convergent. Moreover, the superlinear convergence of the new algorithm is shown without the condition that the Hessian of the objective function at the solution be positive definite. Preliminary numerical results indicate that the performance of the new method is notable.

Keywords: Trust-region methods; trust-region radius; global convergence; superlinear convergence; local error bound. (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10957-006-9053-4

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