### Michael Baes (University of Zurich)

#### Mixed-integer convex optimization: approximations algorithms and duality

*Joint work with Alberto del Pia, Yurii Nesterov, Shmuel Onn, Timm Oertel, Christian Wagner, and Robert Weismantel.*

*Wednesday 26 August 2015 at 15.00, JCMB 4325B*

##### Abstract

The problem of minimizing a convex function over a convex set with the extra
requirement that some variable must be integral, in spite of its intrinsic
difficulty, enjoys enough structural properties to deserve the development of
dedicated solvers. However, most known methods cannot offer any quality
guarantee of the approximate solution they provide after a prescribed time.

In the first part of the talk, I will present two different methodologies to
address this concern, both inspired from first-order methods for purely
convex optimization problems. The results we obtain from these techniques
hint at a general conjecture on the complexity of solving Mixed-Integer
Convex problems approximately. In a second part of the talk, I will show a
new approach for studying duality of mixed-integer convex problems, which
also hint at our general conjecture.

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