Regularization of ill-posed problems with non-negative solutions

2018/05/04 by Clason, Christian, Kaltenbacher, Barbara, Resmerita, Elena
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1805.01722

Abstract

This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or constraints, and iterative methods involving projections or non-negativity-preserving multiplicative updates. We summarize known results and point out some open problems.

Related

• Methods of Solving Ill-Posed Problems
• Regularization of Ill-Posed Problems with Unbounded Operators
• A class of regularization schemes for linear ill-posed problems in Banach spaces under low order source conditions
• Continuous regularization of nonlinear ill-posed problems
• Improved regularizing iterative methods for ill-posed nonlinear systems