We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semideenite matrices. We show that the approach is very eecient for graph bisection problems, such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...

In this paper we present the results obtained in the solution of sparse and large systems of non-linear equations by inexact Newton methods combined with an block iterative row-projection linear solver of Cimmino-type. Moreover, we propose a suitable partitioning of the Jacobian matrix A. In view of the sparsity, we obtain a mutually orthogonal row-partition of A that allows a simple solution o...

Thomas Edison is regarded by many as the greatest inventor in American history. While most people know that he invented the first long-burning incandescent light bulb and the phonograph, the claim is based more generally on the 1093 patents he was granted. The assumption is that the person receiving a patent is legally certified as the inventor of the device which is the subject of the patent. ...

This file of notes serves as a reference for Zeyuan himself about the materials to be delivered in class. It copies a lot of materials from Prof Michel X. Goemans’ lecture notes on 6.854 in 1994, (see http: //www-math.mit.edu/~goemans/notes-lp.ps), and Prof Sven O. Krumke’s report on interior point methods (see http://optimierung.mathematik.uni-kl.de/~krumke/Notes/interior-lecture. pdf). Ye’s i...