Levenberg-Marguardt Trust Region Method
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Date
2016-06
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Addis Ababa University
Abstract
This project addresses the solution of unconstrained optimization problems using
algorithms that require only values with out using derivative (derivative free ) ,the algo-
rithms generate a sequence with an initial point x0 and direction dk and step length
and look for best point (next iteration xk+1 for k=1,2........ in this paper we evaluate four
methods in (derivative free ), cyclic coordinate method , Hooke and Jeeves Mehtod and
Rosenbrock Method and
. The Levenberg-Marquardt method is a standard technique used to solve non-linear least
squares problems. Gradient descent method, the sum of the squared errors is reduced by
updating the parameters . In the Gauss-Newton method, the sum of the squared errors
is reduced by assuming the least squares function is locally quadratic, and it is acts more
like a gradient-descent method when the parameters are far from their optimal value,
and trust region method is technics toand the optimal point within each trust region , the
approach constricts the initial quadratic surrogate model using few of order O(n) ,where
n is the number of design variables , the proposed approach adopts weighted least squares
tting for updating the surrogate model instead of interpolation which is commonly use
In DF optimization , this make the approach more suitable for stochastic optimization
and for functions subject to numerical error . The weights are assigned to give more
emphasis to points close to the current centre point.
Key words: derivative free-optimization , levenberg-Marguardt , trust region method ,
Quadratic surrogate model
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Keywords
Derivative Free-Optimization, Levenberg-Marguardt, Trust Region Method, Quadratic Surrogate Model