## A new trust region algorithm for equality constrained optimization |

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3.l is satisfied According to Algorithm Advanced Computing Research Algorithm 2.1 takes Assumption 4.1 holds c(xk chain rule change of variables Computing Research Institute conditions are satisfied constraint in 1.3 convergence rate CUTE collection denotes described in Lemma eigenvalue exists a constant exists an integer finite number full column rank global convergence Global Optimization implies inequality 2.14 inner loop integer set iterations function evaluations LANCELOT limit points line search necessary optimality conditions nonlinear null space number of iterations number of limit obtain order necessary optimality parameter penalty function point satisfying positive definite problem 1.1 Problem TEST1 problems in Table quadratic approximation quadratic convergence quadratic programming r)dr reduced Hessian matrix s(Zkh satisfies Condition satisfying the second second order necessary solution step length sufficiently large Suppose Assumption 4.1 Taylor's theorem tends to zero test problems TEST1 and TEST2 Theory Center Trust region methods trust region subproblem Zk+h