G.Berhanu (PhD)Fangarasio Arnest2018-07-112023-11-042018-07-112023-11-042016-06http://etd.aau.edu.et/handle/123456789/8036This 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 modelenDerivative Free-OptimizationLevenberg-MarguardtTrust Region MethodQuadratic Surrogate ModelThesis