The Lagrange method for the regularization of discrete ill-posed problems
ABSTRACT In many science and engineering applications, the discretization of linear ill-posed problems gives rise to large ill-conditioned
linear systems with the right-hand side degraded by noise. The solution of such linear systems requires the solution of minimization
problems with one quadratic constraint, depending on an estimate of the variance of the noise. This strategy is known as regularization.
In this work, we propose a modification of the Lagrange method for the solution of the noise constrained regularization problem.
We present the numerical results of test problems, image restoration and medical imaging denoising. Our results indicate that
the proposed Lagrange method is effective and efficient in computing good regularized solutions of ill-conditioned linear
systems and in computing the corresponding Lagrange multipliers. Moreover, our numerical experiments show that the Lagrange
method is computationally convenient. Therefore, the Lagrange method is a promising approach for dealing with ill-posed problems.
Article: The effect of regularization on drug- reaction relationships The effect of regularization on drug-reaction relationships[show abstract] [hide abstract]
ABSTRACT: The least-squares method is a standard approach used in data fitting that has important applications in many areas in science and engineering including many finance problems. In the case when the problem under consideration involves large-scale sparse matrices regularization methods are used to obtain more stable solutions by relaxing the data fitting. In this article, a new regularization algorithm is introduced based on the Karush–Kuhn–Tucker conditions and the Fisher–Burmeister function. The Newton method is used for solving corresponding systems of equations. The advantages of the proposed method has been demonstrated in the establishment of drug-reaction relationships based on the Australian Adverse Drug Reaction Advisory Committee database.Optimization 05/2012; 61:405-422. · 0.50 Impact Factor