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Toint, P.L. (1980) Sparsity Exploiting Quasi-Newton Methods for Unconstrained Optimization. In: Dixon, L.C.W., Spedicato, E. and Szego, G.P., Eds., Nonlinear Optimization: Theory and Algorithms, Birkhauser, Belgium, 65-90.

has been cited by the following article:

• TITLE: A New Nonmonotone Adaptive Trust Region Method

  AUTHORS: Yang Zhang, Quanming Ji, Qinghua Zhou

  KEYWORDS: Unconstrained Optimization, Trust Region Method, Nonmonotone Technique, Global Convergence, Superlinear Convergence

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.12, December 23, 2021

  ABSTRACT: The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.