The paper presents concrete realizations of quasi-Newton methods for solving several standard problems including complementarity problems, special variational inequality problems, and the Karush–Kuhn–Tucker (KKT) system of nonlinear programming. A new approximation idea is introduced in this paper. The Q-superlinear convergence of the Newton method and the quasiNewton method are established und...

We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms sξ , sξ , s (c) ξ , or lp(ξ). Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear ...

In this work, we address the implementation and performance of inexact Newton-Krylov quasi-Newton algorithms, more specifically BFGS method, for solution nonlinear elasticity equations, compare them to a standard method. This is done through systematic analysis solvers with respect problem size, magnitude data number processors in both almost incompressible mechanics. We consider three test cas...