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30 April 2012
15:00-16:00

Prof. Dr. Yurii Nesterov
Catholic University of Louvain, Louvain-la-Neuve, Belgium

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Title	Subgradient methods for huge-scale optimization problems
Speaker, Affiliation	Prof. Dr. Yurii Nesterov, Catholic University of Louvain, Louvain-la-Neuve, Belgium
Date, Time	30 April 2012, 15:00-16:00
Location	HG G 19.1
Abstract	We consider a new class of huge-scale problems, the problems with sparse subgradients. The most important functions of this type are piece-wise linear. For optimization problems with uniform sparsity of corresponding linear operators, we suggest a very efficient implementation of subgradient iterations, which total cost depends logarithmically in the dimension. This technique is based on a recursive update of the results of matrix/vector products and the values of symmetric functions. It works well, for example, for matrices with few nonzero diagonals and for max-type functions. We show that the updating technique can be efficiently coupled with the simplest subgradient methods, the unconstrained minimization method by B. Polyak, and the constrained minimization scheme by N. Shor. Similar results can be obtained for a new non- smooth random variant of a coordinate descent scheme. We present also the promising results of preliminary computational experiments.

Subgradient methods for huge-scale optimization problemsread_more

20 June 2012
11:15-12:00

Prof. Dr. Pietro Belotti
Clemson University, Dept. of Mathematical Sciences, Clemson, USA

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Title	Heuristics for Integer Nonlinear Optimization
Speaker, Affiliation	Prof. Dr. Pietro Belotti, Clemson University, Dept. of Mathematical Sciences, Clemson, USA
Date, Time	20 June 2012, 11:15-12:00
Location	HG G 19.2
Abstract	Mixed Integer Nonlinear Programming (MINLP) problems consist of minimizing a nonlinear function subject to nonlinear constraints and the integrality of a subset of variables. These problems can be solved by branch-and-bound algorithms equipped with procedures that reduce the solution space and allow to find good lower bounds on the optimal solution. Finding good feasible solutions is equally important and just as difficult, as one deals with two types of nonconvexity: nonlinear constraints and integrality of some variables. Inspired by a technique that proved successful in Mixed Integer Linear problems, we have developed a variant of the Feasibility Pump for MINLPs. Unlike some previous extensions of the Feasibility Pump to MINLP, our version uses a valid relaxation of the MINLP problem provided by Couenne, an Open-Source solver for MINLPs available from the COIN-OR initiative. We present results on mid-size and large MINLP instances available from well-known instance libraries. (Joint work with Timo Berthold, Zuse Institute Berlin)

Heuristics for Integer Nonlinear Optimizationread_more

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