This paper explores the convergence of trust region methods for constrained minimization of differentiable function.In the first part, two trust region algorithms for linearly constrained optimization problem are proposed 1)Combining quasi-Newton and trust region method for linearly equality constrained optimization is given , its global convergence and super-linear rate is proved. 2) Interior-point trust region algorithm for box constrained problem and its global convergence. In the second part , a non-monotone trust region algorithm for non-linearly equality constrained optimization problem is proposed and its global convergence and super-linear rate is proved. |