Solving trust-region subproblem augmented with linear inequality constraints

Abstract

In this work, we present a new algorithm for solving the augmented trust-region subproblem with a set of additional linear inequality constraints. The method can be considered as a generalization of previously published method [M. Rojas and T. Steihaug, An interior-point trust-region-based method for large-scale non-negative regularization, Inverse Problems 18(5) (2002), pp. 1291–1307]. We discuss the additional types of problems our formulation can solve and reproduce regularized large-scale inverse-problem results from image processing in our general framework.

Keywords:

• constrained optimization
• regularization
• image processing

Acknowledgements

We wish to thank Marielba Rojas for a wide range of comments which greatly improved the article.