We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with ...

Efficient handling of inexact (grey) information is an important issue for the new emerging database technology. Inexact or imprecise information has been represented and manipulated by using different techniques, including fuzzy set theory, possibility theory, IVF (Interval Valued Fuzzy) Sets, Time Petri Nets, Fuzzy Clouds, etc. In this paper, different approaches dealing with uncertainty have...

This paper studies an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale separable convex programming problems. Unlike the exact versions considered in the literature, we propose to solve the primal subproblems inexactly up to a given accuracy. This leads to an inexactness of the gradient vector and the Hessian matrix of the smoo...

Pattern matching occurs in various applications, ranging from simple text searching in word processors to identification of common motifs in DNA sequences in computational biology. The problem of exact pattern matching has been well studied and a number of efficient algorithms exist. However these exact pattern matching algorithms are of little help when they are applied to finding patterns in ...

In this paper, we survey some of the latest development in using inexact Newton-like methods for solving inverse eigenvalue problems. These methods require the solutions of nonsymmetric and large linear systems. One can solve the approximate Jacobian equation by iterative methods. However, iterative methods usually oversolve the problem in the sense that they require far more (inner) iterations...

This work takes advantage of the spectral projected gradient direction within the inexact restoration framework to address nonlinear optimization problems with nonconvex constraints. The proposed strategy includes a convenient handling of the constraints, together with nonmonotonic features to speed up convergence. The numerical performance is assessed by experiments with hard-spheres problems,...