Scientific Program

Semi-plenary Lecture

Program -> Plenary and Semi-Plenary -> Wed.17:00.H 0105 title only | abstract | bio sketch

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.

 

 

Program -> Plenary and Semi-Plenary -> Wed.17:00.H 0105 title only | abstract | bio sketch

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