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...

2 Methods 2 2.1 Lagrange Multiplier Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Pegging Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Interior-Point Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.2 Interior-Point Algorithm ....

Hardware information: Any computer with a FORTRAN 77 compiler.

We present complexity results on solving real-number standard linear programs LP (A,b, c), where the constraint matrix A ∈ IRm×n, the right-hand-side vector b ∈ IR and the objective coefficient vector c ∈ IR are real. In particular, we present a two-layered interior-point method and show that LP (A,b,0), i.e., the linear feasibility problem Ax = b and x ≥ 0, can be solved in in O(n2.5c(A)) inte...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...

Abstract. Sampling points from the uniform distribution on a polytope is a well-studied problem, and is an important ingredient in several computational tasks involving polytopes, such as volume estimation. This is achieved by setting up a random walk inside the polytope, with its stationary distribution being uniform in the interior of the polytope. Kannan-Narayanan [6] and Narayanan [9] propo...