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

Abstract

This paper presents a multi-objective optimization approach for choosing an appropriate regularization parameter in Tikhonov-type regularization of discrete ill-posed problems. Finding the regularization parameter is formulated as a multi-objective optimization problem and some transformations are introduced to construct a new problem equivalent to it. Then, by using the standard multi-objective optimization methods, a single-objective problem is derived that its minimizer gives a proper estimation of the regularization parameter. Via considering some test problems, the numerical efficiency of the presented method is compared with the L-curve and the GCV parameter choice methods.