Abstract: A trust region algorithm is presented for solving optimization problem with equality constraints The algorithm uses the Byrd and Omojokun scheme to compute the steps,and decomposes the trial steps into two components:normal component and tangential component But it differs from the Byrd and Omojokun algorithm with a reduced dimension approach in computing each tangential component Global convergence can be proved under some mild assumptions.

Key words: optimization, trial step, global convergence, trust region method, exact penalty functions