In this project, we propose a trust region dogleg method algorithms tornsolve a trust region subproblems arising form unconstrained optimization.rnThe method can deal with by constricting a dogleg paths. The case whenrnthe Hessian B of quadratic models is positive de nite. The philosophy andrnfundamental ideas of trust region algorithms are discussed and proved thatrnthe method is globally convergent and has a supper linear convergence rate.rnAnd then the nal algorithm is programmed in MATLAB and implementedrnby taking appropriate test problem.