Improvements to the cluster Newton method for underdetermined inverse problems

• Published in: Journal of computational and applied mathematics Vol. 283; pp. 122 - 141
• Main Authors: Gaudreau, P., Hayami, K., Aoki, Y., Safouhi, H., Konagaya, A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2015
• Subjects: Algorithms; Beta distribution; Cluster Newton method; Clusters; Inverse problems; Jacobians; Matematik med inriktning mot tillämpad matematik; Mathematical analysis; Mathematical models; Mathematics with specialization in Applied Mathematics; Newton methods; Pharmacokinetics; Tasks; Underdetermined inverse problem; Beta distribution; Underdetermined inverse problem; Cluster Newton method; Pharmacokinetics
• ISSN: 0377-0427; 1879-1778; 1879-1778
• DOI: 10.1016/j.cam.2015.01.014

The Cluster Newton method (CN method) has proved to be very efficient at finding multiple solutions to underdetermined inverse problems. In the case of pharmacokinetics, underdetermined inverse problems are often given extra constraints to restrain the variety of solutions. In this paper, we propose a new algorithm based on the two parameters of the Beta distribution for finding a family of solutions which best fit the extra constraints. This allows for a much greater control on the variety of solutions that can be obtained with the CN method. In addition, this algorithm facilitates the task of obtaining pharmacologically feasible parameters. Moreover, we also make some improvements to the original CN method including an adaptive margin of error for the perturbation of the target values and the use of an analytical Jacobian in the resolution of the forward problem.