In this paper we introduce a local convergence theory for Least Change Secant Update methods. This theory includes most known methods of this class, as well as some new interesting quasi-Newton methods. Further, we prove that this class of LCSU updates may be used to generate iterative linear methods to solve the Newton linear equation in the Inexact-Newton context. Convergence at a ¡j-superlin...

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...

Convergence results are provided for inexact inverse subspace iteration applied to the problem of finding the invariant subspace associated with a small number of eigenvalues of a large sparse matrix. These results are illustrated by the use of block-GMRES as the iterative solver. The costs of the inexact solves are measured by the number of inner iterations needed by the iterative solver at ea...

In this paper we present a hybrid path-following algorithm that generates inexact Newton steps suited for solving large scale and/or degenerate nonlinear programs. The algorithm uses as a central region a relaxed notion of the central path, called quasicentral path, a generalized augmented Lagrangian function, weighted proximity measures, and a linesearch within a trust region strategy. We appl...

We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using itera...

As an extension of the inexact Uzawa algorithm addressed in 1], we propose an improved inexact Uzawa-type iterative method for solving saddle point problems. The convergence rate is given in terms of the rates of the two basic iterations as deened in 1], and it is shown that the new algorithm always converges as long as the two basic iterations converge. A running title: Uzawa algorithm for sad...

We consider an implicit iterative method in convex programming which combines inexact variants of the proximal point algorithm, with parametric penalty functions. We investigate a multiplier sequence which is explicitly computed in terms of the primal sequence generated by the iterative method, providing some conditions on the parameters in order to ensure convergence towards a particular dual ...