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Dennis, J.E. and Mei, H.H.W. (1979) Two New Unconstrained Optimization Algorithms Which Use Function and Gradient Values. Journal of Optimization Theory and Applications, 28, 453-482. https://doi.org/10.1007/BF00932218

has been cited by the following article:

• TITLE: An Algorithm for the Derivative-Free Unconstrained Optimization Based on a Moving Random Cone Data Set

  AUTHORS: Mariam Almahdi Mohammed Mu’lla

  KEYWORDS: Optimization Problem, Convergence, Trust-Region Methods, Model-Based Optimization, Derivative-Free Optimization, Interpolation Examples

  JOURNAL NAME: Open Access Library Journal, Vol.6 No.9, September 10, 2019

  ABSTRACT: In this paper, we suggest and analyze some new derivative free iterative methods for solving nonlinear equation using a trust-region method. We also, give several examples to illustrate the efficiency of these methods. Comparison with other similar method is also given. This tech-nique can be used to suggest a wide class of new iterative methods for solving optimization problem. For, solving linearly unconstrained optimi-zation problems without derivatives, a derivative-free Funnel method for unconstrained non-linear optimization is proposed. The study presents new interpolation-based techniques. The main work of this paper depends on some matrix computation techniques. A linear system is solved to obtain the required quadratic model at each iteration. Interpolation points are based on polynomial which is then minimized in a trust-region.