Determination of regularization parameter via solving a multi-objective optimization problem (Q2189712)

Regularization methods play a significant role in the study of inverse and ill-posed problems. For optimization reformulation of an inverse or ill-posed problem, a regularization procedure consists of replacing the optimization problem with a family of regularized problems parameterized by the regularization parameter. Since a proper selection of the regularization parameter is crucial, numerous methods are now available to estimate the optimal parameter under varying conditions. This paper studies a discrete ill-posed problem in the least-squares type optimization formulation. The authors propose a new method for estimating the optimal regularization parameter by viewing the regularized problem as a bi-criteria/multi-objective optimization problem. Theoretical results embark on the Pareto optimality of the regularized solution and the regularization parameter's impact on the components of the multi-objective optimization problem. The authors report detailed numerical experimentation and compare the proposed scheme with the L-curve and GCV method. This paper should be of interest to the vector optimization and inverse problems communities.