In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F(x) = 0; by a Quasi-Newton method combined with a p block iterative row-projection linear solver of Cimmino-type, 1 p n: Under weak regularity conditions for F; it is proved that this Inexact Quasi-Newton method has a local, linear convergence in the energy norm induced by the preconditi...

Newton and quasi-Newton methods have been used in chemical process design and optimization calculations for quite some time. They continue to be used today, both in the traditional sense and as part of the more recent hybrid method. While Newton-based fixed-point methods have been used to solve many different kinds of chemical process design and optimization problems, perhaps the point of singl...

Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to “lag” the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which...

Most existing quasi-Newton methods for nonlinear least squares problems incorporate both linear and nonlinear information in the secant update. These methods exhibit good theoretical properties, but are not especially accurate in practice. The objective of this paper is to propose quasi-Newton methods that only update the nonlinearities. We show two advantages of such updates. First, fast conve...

It is well known that the conjugate gradient method and a quasi-Newton method, using any well-defined update matrix from the one-parameter Broyden family of updates, produce the same iterates on a quadratic problem with positive-definite Hessian. This equivalence does not hold for any quasi-Newton method. We discuss more precisely the conditions on the update matrix that give rise to this behav...

A new conjugate gradient method is proposed for applying Powell's symmetrical technique to conjugate gradient methods in this paper, which satisfies the sufficient descent property for any line search. Using Wolfe line searches, the global convergence of the method is derived from the spectral analysis of the conjugate gradient iteration matrix and Zoutendijk's condition. Based on this, two con...

The quasi-newton methods are one of the most effective for solving unconstrained optimization problems. This letter provides a hardware-efficient massive multiple-input multiple-output (MIMO) detector using an improved (IQN) method. Due to similarity in stepsize calculation Barzilai-Borwein and limited-memory BFGS, two deeply fused proposed IQN algorithm higher convergence speed. corresponding ...