A numerical method with the approximate global convergence property is developed for a 3-D Coefficient Inverse Problem for a hyperbolic PDE with the backscattering data. An important part of this technique is the quasi-reversibility method. Approximate global convergence theorem is proven. Results of two numerical experiments are presented.

In this paper, we investigate global convergence properties of the inexact nonsmooth Newton method for solving the system of absolute value equations (AVE). Global Q-linear convergence is established under suitable assumptions. Moreover, we present some numerical experiments designed to investigate the practical viability of the proposed scheme.

In a recent paper, Dennis, El-Alem, and Maciel suggested a class of trust-region-based algorithms for solving the equality constrained optimization problem. They proved global convergence for the class. In this paper, we characterize this class and present a short, straightforward, and self-contained global convergence theory. The results are stronger than Dennis, El-Alem, and Maciel's results.