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...

We consider the problem of fitting linearly parameterized models, that arises in many computer vision problems such as road scene analysis. Data extracted from images usually contain non-Gaussian noise and outliers, which makes non-robust estimation methods ineffective. In this paper, we propose an overview of a Lagrangian formulation of the Half-Quadratic approach by, first, revisiting the der...

in this paper, we propose the least-squares method for computing the positive solution of a m  n fully fuzzy linear system (ffls) of equations, where m > n, based on kaman's arithmetic operations on fuzzy numbers that introduced in [18]. first, we consider all elements of coecient matrix are non-negative or non-positive. also, we obtain 1-cut of the fuzzy number vector solution of the n...

In this paper, we investigate the nite element method for numerically identifying physical parameters in parabolic initial-boundary value problems. The identifying problem is rst formulated as a constrained minimization problem using the output least squares approach with the H 1-regularization or BV-regularization. Then a simple nite element method is used to approximate the constrained minimi...

We report some experience with optimization methods applied to an inverse light scattering problem for spherical, homogeneous particles. Such particles can be identified from experimental data using a least squares global optimization method. However, if there is significant noise in the data, the “best” solution may not correspond well to the “actual” particle. We suggest a way in which the or...

The total least squares (TLS) method is an appropriate approach for linear systems when not only the right-hand side but also the system matrix is contaminated by some noise. For ill-posed problems regularization is necessary to stabilize the computed solutions. In this presentation we discuss two approaches for regularizing large scale TLS problems. One which is based on adding a quadratic con...