The generalized eigenvalue problem

We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...

This paper presents a practical and efficient method to solve large-scale nonlinear equations. The global convergence of this new trust region algorithm is verified. The algorithm is then used to solve the nonlinear equations arising in an Expanded Lagrangian Function (ELF). Numerical results for the implementation of some large-scale problems indicate that the algorithm is efficient for these ...

Non monotone algorithms allow a possible increase of function values at certain iterations. This paper gives a suitable control on this increase to preserve the convergence properties of its monotone counterpart. A new efficient MultiLineal Search is also proposed for minimization algorithms. keywords: Non Monotone, Lineal Search, Trust Region.

Optimization methods based on iterative schemes can be divided into two classes: linesearch methods and trustregion methods. While linesearch techniques are commonly found in various vision applications, not much attention is paid to trust-region methods. Motivated by the fact that linesearch methods can be considered as special cases of trust-region methods, we propose to apply trust-region me...

Nowadays, peer-to-peer (P2P) streaming systems have become a 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 exploring...

Abstract. We consider methods for large-scale unconstrained minimization based on finding an approximate minimizer of a quadratic function subject to a two-norm trust-region inequality constraint. The Steihaug-Toint method uses the conjugate-gradient algorithm to minimize the quadratic over a sequence of expanding subspaces until the iterates either converge to an interior point or cross the co...