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X.-L. Luo, C. T. Kelley, L.-Z. Liao and H. W. Tam, “Combining Trust Region Techniques and Rosenbrock Methods to Compute Stationary Points,” Journal of Optimization Theory and Applications, Vol. 140, No. 2, 2009, pp. 265-286. doi:10.1007/s10957-008-9469-0

has been cited by the following article:

• TITLE: A New Technique for Estimating the Lower Bound of the Trust-Region Subproblem

  AUTHORS: Xinlong Luo

  KEYWORDS: Trust-Region Method, Unconstrained Optimization, Trust-Region Subproblem

  JOURNAL NAME: Applied Mathematics, Vol.2 No.4, March 31, 2011

  ABSTRACT: Trust-region methods are popular for nonlinear optimization problems. How to determine the predicted reduction of the trust-region subproblem is a key issue for trust-region methods. Powell gave an estimation of the lower bound of the trust-region subproblem by considering the negative gradient direction. In this article, we give an alternate way to estimate the same lower bound of the trust-region subproblem.