AN INTERIOR TRUST REGION APPROACH FOR NONLINEAR MINIMIZATION SUBJECT TO BOUNDS

We propose a new trust region approach for minimizing a nonlinear func tion subject to simple bounds. Unlike most existing methods, our propo sed method does not require that a quadratic programming subproblem, w ith inequality constraints, be solved in each iteration. Instead, a so lution to a trust region subproblem is defined by minimizing a quadrat ic function subject only to an ellipsoidal constraint. The iterates ge nerated are strictly feasible. Our proposed method reduces to a standa rd trust region approach for the unconstrained problem when there are no upper or lower bounds on the variables. Global and local quadratic convergence is established. Preliminary numerical experiments are repo rted indicating the practical viability of this approach.