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.