Trust-region algorithms have been proved to globally converge with probability one when the accuracy of the trust-region models is imposed with a certain probability conditioning on the iteration history. In this paper, we study their complexity, providing global rates and worst case complexity bounds on the number of iterations (with overwhelmingly high probability), for both first and second ...

Nowadays, peer-to-peer (P2P) streaming systems have become the most popular way to deliver multimedia content over the internet due to their low bandwidth requirement, high video streaming quality, and flexibility. However, P2P streaming systems are vulnerable to various attacks, especially pollution attacks, due to their distributed and dynamically changing infrastructure. In this paper, by ex...

In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences , by a trust region-cg algorithm. Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Our basic technique is the so-called trust region method, while ...

Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function va...