An interior-point trust-region-based method for large-scale non-negative regularization

We present a new method for large-scale non-negative regularization based on a quadratically and non-negatively constrained quadratic problem. Such problems arise for example in the regularization of ill posed problems in image restoration where 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 parametrized trust-region subproblem 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.