Abstarct: In this thesis, we first introduce the basic ‎concepts‎ and preliminaries. Then, we express the concepts of the efficiency and weak efficiency for multiobjective optimization problem. ‎We deal to solve multiobjective optimization problem b‎y applying iterative methods.‎ An iterative method is a computational process that generates a sequence and we expect that under reasonable conditions converges to the efficient solution of the problem.‎‎ From the iterative methods for multiobjective optimization problem, we discuss, the Newton method and the quasi-Newton methods. Following, we express the Newton algorithm for solving convex multiobjective optimization problem that requires precise calculation of the Hessian matrix for each objective function. ‎ In the case that calculation of the Hussein be difficult, quasi-Newton methods are introduced and are discussed. These methods calculate the Hessian approximate instead of the exact Hessian and help us to improve the solving process.‎ In cases where the problem is nonconvex, a modified quasi-Newton algorithm is suggested. ‎ In this‎ case, by calculating an approximate matrix, nonconvex multiobjective problems are solved. Finally, a‎ ‎‎quasi-Newton method for solving nonsmooth multiobjective problem is introduced.