## Scientific Program

### Semi-plenary Lecture

**Wednesday, 17:00 - 17:50 h, H 0105**

Robert Weismantel

**Mixed Integer Convex Optimization**

Chair: Gérard Cornuéjols

**Abstract:**

This talk deals with algorithms and complexity results about the minimization of convex functions over integer points in convex regions.

We begin with a survey about the current state of art.

Then we discuss results about to the speed of convergence of a black box algorithm that iteratively solves special quadratic integer subproblems with a constant approximation factor. Despite the generality of the underlying problem we prove that we can detect efficiently w.r.t. our assumptions regarding the encoding of the problem a feasible solution whose objective function value is close to the optimal value.

We also show that this proximity result is best possible up to a polynomial factor.

Next we discuss a new "cone-shrinking algorithm" that allows us to prove that integer convex optimization with a constant number of variables is polynomial time solvable.

Parts of our results are based on joint work with M. Baes, A. del Pia, Y. Nesterov, S. Onn. The other part is based on joint work with M. Baes, T. Oertel, C. Wagner.

**Biographical sketch:**

Robert Weismantel was born in 1965 in München, Germany. After studying mathematics at the University of Augsburg, he moved with Martin Grötschel to the Konrad-Zuse-Zentrum für Informationstechnik in Berlin (ZIB) in 1991. From the TU Berlin he received his PhD degree in 1992 and his second PhD degree (Habilitation) in 1995.

In the years 1991 - 1997 he was a researcher at ZIB. From 1998 to 2010 he was a Professor (C4) for Mathematical Optimization at the University of Magdeburg. In 2010, he was elected Full Professor at the Department of Mathematics at ETH Zurich.

His main research interest is integer and mixed integer optimization:

specifically he was working on primal integer programming, the theory of Hilbert bases, and cutting plane theory. More recently he is working on nonlinear integer optimization.

His work has been distinguished with several prizes and honors:

His PhD thesis was awarded a Carl Ramsauer Prize. He received the Gerhard Hess Research Prize of the German Science Foundation and IBM-Faculty Awards in 2007 and 2010. He is currently a Co-Editor of Mathematical Programming A.