This project addresses the solution of unconstrained optimization problems usingrnalgorithms that require only values with out using derivative (derivative free ) ,the algo-rnrithms generate a sequence with an initial point x0 and direction dk and step length rnand look for best point (next iteration xk+1 for k=1,2........ in this paper we evaluate fourrnmethods in (derivative free ), cyclic coordinate method , Hooke and Jeeves Mehtod andrnRosenbrock Method andrn. The Levenberg-Marquardt method is a standard technique used to solve non-linear leastrnsquares problems. Gradient descent method, the sum of the squared errors is reduced byrnupdating the parameters . In the Gauss-Newton method, the sum of the squared errorsrnis reduced by assuming the least squares function is locally quadratic, and it is acts morernlike a gradient-descent method when the parameters are far from their optimal value,rnand trust region method is technics toand the optimal point within each trust region , thernapproach constricts the initial quadratic surrogate model using few of order O(n) ,wherernn is the number of design variables , the proposed approach adopts weighted least squaresrntting for updating the surrogate model instead of interpolation which is commonly usernIn DF optimization , this make the approach more suitable for stochastic optimizationrnand for functions subject to numerical error . The weights are assigned to give morernemphasis to points close to the current centre point.rnKey words: derivative free-optimization , levenberg-Marguardt , trust region method ,rnQuadratic surrogate model