Guta, Berhanu (PhD)Leul, Hewan2019-04-082023-11-092019-04-082023-11-092018-06-03http://etd.aau.edu.et/handle/123456789/17644In this project we give trust-region algorithms for nonlinear optimization. Trust-region methods are robust and can be applied to ill-conditioned problems. A conjugate gradient trust-region algorithm is presented to demonstrate the trust region approaches. Conver- gence properties of trust-region with conjugate gradient are given. A trust-region method subproblems for solving unconstrained optimization is proposed. At every iteration, we use the conjugate gradient method or its variation to solve the subproblems approximately. We show that this method has the same convergence properties as the trust-region method based on the conjugate gradient method. Numerical results show that this method is as reliable and more e cient in respect of iterations and evaluations using MATLAB.enLine SearchNewton MethodSteepest DescentConjugate GradientTrust- RegionThesis