报告主题： A new method for solving the homogeneous feasibility problem
报告人：Kees Roos 教授 （荷兰 Delft University of Technology）
报告摘要：Finding a nonnegative nonzero vector in the null space of a matrix is a fundamen-tal problem that arises in many applications. The same holds for its dual problem,which is the problem of finding a positive vector in the row space of a matrix. The first problem is called the Von Neumann problem, after John von Neumann, who proposed the first solution method in a private communication to George Dantzig in 1948; it has been published by Dantzig only in 1992. The second problem is the so-called Perceptron problem. The perceptron models a hypothetical nervous system, or machine, and is designed to illustrate some of the fundamental properties of intelligent systems. Nowadays both problems find much interest in Artificial Intelligence, especiallyin Big Data and Machine Learning. Usually the problems that arise are so large that the standard methods for solving linear optimization problems (like the Sim-plex Method and Interior-Point Methods) fail to work. Therefore the emphasis is currently on the use of cleverly designed first-order methods. In our presentation we fucus on a new method that combines the Mirror-Prox method of Nemirovski and a rescaling method introduced by Chubanov.