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Copositive optimization, the copositive cone, and its relation with Parrilo's approximations

A copositive optimization problem is a linear problem in matrix variables with the additional constraint that the variable is in the cone of copositive matrices. Here a matrix A is called copositive if the quadratic form (x^T)Ax is nonnegative for all nonnegative x. Copositive optimization problems are of interest, because many quadratic as well as combinatorial problems can be written in this form. A well studied example is the maximum clique problem from graph theory. However, the structure of the copositive cone is not well understood, and in general copositive problems are not tractable. For this reason, a number of relaxations have been proposed, among them a hierarchy of approximating cones was proposed by Parrilo. The talk will give an introduction to these topics and place particular emphasis on the relation between the cone and Parrilo's approximations.

Type of Seminar:
Optimization and Applications Seminar
Prof. Mirjam Dür
Department of Mathematics, University of Trier
Oct 08, 2012   16:30

HG G 19.1
Contact Person:

John Lygeros
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Biographical Sketch:
Mirjam Dür was born in Vienna, Austria, where she received a M.Sc. degree in Mathematics from the University of Vienna in 1996. She received a PhD in applied mathematics from University of Trier in 1999. After that, she worked as an assistant professor at Vienna University of Economics and Business Administration, as a junior professor at TU Darmstadt, and as an Universitair Docent at the University of Groningen, The Netherlands. Since October 2011, she is a professor of Nonlinear Optimization in Trier. Dr. Dür is member of the editorial boards of Mathematical Methods of Operations Research, Journal of Global Optimization, and Optimization Methods and Software. In 2010, she was awarded a VICI-grant by the Dutch Organisation for Scientific Research (NWO).