Globally convergent variants of the Gauss--Newton algorithm are often methods choice to tackle nonlinear least-squares problems. Among such frameworks, Levenberg--Marquardt and trust-region two well-established, similar paradigms. Both schemes have been studied when model is replaced by a random that only accurate with given probability. Trust-region also applied problems where objective value ...

Abstract A new Levenberg–Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM have been proposed, their main differences being in choice a damping parameter. In this paper, we propose rule updating parameter so as to achieve both global and local convergence even under presence constraint set. The key our results per...

The treatment planning software TRiP98 [1, 2, 3] is successfully used in the ion therapy project at GSI. A crucial part of the treatment planning is the particle number optimization in order to achieve a target dose distribution as close as possible to the prescribed biological dose distribution. The optimization task can be expressed mathematically by the minimization of a multidimensional obj...

This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the qu...

In this paper, we propose the block-diagonal matrix to approximate the Hessian matrix in the Levenberg Mar-quardt method in the training of neural networks. Two weight updating strategies, namely asynchronous and synchronous updating methods were investigated. Asyn-chronous method updates weights of one block at a time while synchronous method updates all weights at the same time. Variations of...

Well logging inversion was carried out using Levenberg-Marquardt (LM) and Singular Value Decomposition (SVD) techniques for the determination of petrophysical parameters, respectively. In this research, synthetic data contaminated with 5% Gaussian noise, field were used to compare results from two methods. MATLAB software has been developed solve overdetermined inverse problem. The estimated pa...

In this paper, we study convergence properties of the inexact Levenberg-Marquardt method under Hölderian local error bound condition and continuity Jacobian. The formula rates are given, which functions with respect to parameter, perturbation vector, as well orders