A trust-region algorithm for equality-constrained optimization via a reduced dimension approach

A trust-region algorithm is presented for solving optimization problem with equality constraints. The algorithm uses the Byrd–Omojokun scheme to compute the steps, and decompose the trial steps into two components: normal component and tangential component. But it differs from the Byrd–Omojokun algorithm with a reduced dimension approach in computing each tangential component. Global convergence of the proposed algorithm is proved under some mild assumptions. Three numerical examples are given to illustrate the efficiency of the algorithm.