This paper presents a trust region method for minimizing a nonlinear function subject to bounds. The method uses a quadratic model and scaling matrix to avoid solving a quadratic programming subproblem with linear inequalities. Instead, it solves a trust region subproblem with an ellipsoidal constraint. The iterates generated by the method are always strictly feasible. The method reduces to a standard trust region approach for the unconstrained problem when there are no bounds on the variables. The method is shown to have global and quadratic convergence properties. Preliminary numerical experiments are reported. The method is motivated by examining the optimality conditions for the bound-constrained problem. The method is based on a diagonal system of nonlinear equations and uses a Newton step for the system. The method is shown to have reasonable convergence properties under the nondegeneracy assumption. The method is compared to other trust region methods and is shown to be more efficient. The method is also shown to be practical and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The methodThis paper presents a trust region method for minimizing a nonlinear function subject to bounds. The method uses a quadratic model and scaling matrix to avoid solving a quadratic programming subproblem with linear inequalities. Instead, it solves a trust region subproblem with an ellipsoidal constraint. The iterates generated by the method are always strictly feasible. The method reduces to a standard trust region approach for the unconstrained problem when there are no bounds on the variables. The method is shown to have global and quadratic convergence properties. Preliminary numerical experiments are reported. The method is motivated by examining the optimality conditions for the bound-constrained problem. The method is based on a diagonal system of nonlinear equations and uses a Newton step for the system. The method is shown to have reasonable convergence properties under the nondegeneracy assumption. The method is compared to other trust region methods and is shown to be more efficient. The method is also shown to be practical and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method is proven to have global and quadratic convergence properties. The method is shown to be effective for small dense problems. The method is also shown to be robust and can be used for large problems. The method