In this paper we consider the composite self-concordant (CSC) minimization problem, which minimizes the sum of a self-concordant function f and a (possibly nonsmooth) proper closed convex function g. The CSC minimization is the cornerstone of the path-following interior point methods for solving a broad class of convex optimization problems. It has also found numerous applications in machine le...

We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties.

Fluid-structure interaction problems arise in many fields of application such as flows around elastic structures or blood flow in arteries. The method presented in this paper for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincaré operators. This interface equation is solved by a Newton iteration, for which directional derivat...

1 Student of Department of Electronics & Communication Engineering, 2 Professor, Department of Mathematics, 1,2 R. V. College of Engineering, Mysore Road, Bangalore, Karnataka-560 059, INDIA __________________________________________________________________________________________ Abstract: New iterative algorithms for finding the nth root of a positive number m, to any degree of accuracy, are ...

A NEW multigrid relaxation scheme is developed for the steady-state solution of the Euler and Navier-Stokes equations. The lower-upper Symmetric-Gauss-Seidel method (LUSGS) does not require flux splitting for approximate Newton iteration. The present method, which is vectorizable and unconditionally stable, needs only scalar diagonal inversions. Application to transonic flow shows that the new ...

The multivariate eigenvalue problem (MEP) which originally arises from the canonical correlation analysis is an important generalization of the classical eigenvalue problem. Recently, the MEP also finds applications in many other areas and continues to receive interest. However, the existing algorithms for the MEP are the generalization of the power iteration for the classical eigenvalue proble...

In this paper, we consider the least squares semidefinite programming with a large number of equality and inequality constraints. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. In this paper, we propose to overcome this difficulty by reformulating the problem as a system of semismooth equations with two level metric p...

We propose a Newton method for solving smooth unconstrained vector optimization problems under partial orders induced by general closed convex pointed cones. The method extends the one proposed by Fliege, Graña Drummond and Svaiter for multicriteria, which in turn is an extension of the classical Newton method for scalar optimization. The steplength is chosen by means of an Armijo-like rule, gu...

In this paper, we suggest and analyze a new family of iterative methods for finding zeros of multiplicity of nonlinear equations by using the variational iteration technique. These new methods include the Halley method and its variants forms as special cases. We also give several examples to illustrate the efficiency of these methods. Comparison with modified Newton method is also given. These ...

We consider the inverse problem for an elastic body emerged in a fluid due to an acoustic wave. The shape of this obstacle is to be reconstructed from the far-field pattern of the scattered wave. For the numerical solution in the two-dimensional case, we compare a simple Newton type iteration method with the Kirsch–Kress algorithm. Our computational tests reveal that the Kirsch–Kress method con...