An Interior-Point Trust-Region-Based Method for Large-Scale Nonnegative Regularization

We present a new method for large-scale nonnegative regularization, based on a quadratically and nonnegatively constrained quadratic problem. Such problems arise for example in the regularization of ill-posed problems in image restoration where, in addition, some of the matrices involved are very ill-conditioned. The method is an interior-point iteration that requires the solution of a large-scale and possibly ill-conditioned parameterized trust-region subproblems at each step. The method uses recently developed techniques for the large-scale trust-region subproblem. We describe the method and present preliminary numerical results on test problems and image restoration problems. AMS classification: Primary: 86A22. Secondary: 65K10, 90C06