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

DOI: 10.4236/oalib.1105652, PP. 1-11

Subject Areas: Mathematical Logic and Foundation of Mathematics, Mathematical Analysis

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

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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.

Cite this paper

Mu’lla, M. A. M. (2019). An Algorithm for the Derivative-Free Unconstrained Optimization Based on a Moving Random Cone Data Set. Open Access Library Journal, 6, e5652. doi: http://dx.doi.org/10.4236/oalib.1105652.

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