M. J. D. Powell, “Convergence Properties of a Class of Minimization Algorithms,” In: O. L. Mangasarian, R. R. Meyer and S. M. Robinson Eds., Nonlinear Programming 2, Academic Press, New York, 1975, pp. 1-27.

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.