Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 08, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Jiří Matoušek (Charles Univ., Prague)

On the difficulty of removing degeneracy in LP-type problems: The way of topology

LP-type problems is a successful axiomatic framework for optimization problems capturing, e.g., linear programming and the smallest enclosing ball of a point set. With Petr Škovroň we proved that in order to remove degeneracies of an LP-type problem, we sometimes have to increase its combinatorial dimension by a multiplicative factor of at least 1+epsilon for a certain small positive constant epsilon. The proof went by checking the unsolvability of a system of linear inequalities, with several pages of calculations. Here I will discuss a short topological proof showing that the dimension sometimes has to increase at least twice.

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