Shaban, Arnest Fangarasio (2016) Levenberg-Marguardt Trust Region Method. Masters thesis, Addis Ababa University.
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Abstract
This project addresses the solution of unconstrained optimization problems using algorithms that require only values with out using derivative (derivative free ) ,the algorithms generate a sequence with an initial point x0 and direction dk and step length λ 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 to find 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 fitting 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.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | derivative free-optimization , levenberg-Marguardt , trust region method , Quadratic surrogate model |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Divisions: | Africana |
| Depositing User: | Selom Ghislain |
| Date Deposited: | 15 Aug 2018 13:26 |
| Last Modified: | 15 Aug 2018 13:26 |
| URI: | http://thesisbank.jhia.ac.ke/id/eprint/4844 |
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