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The Minimum Euclidean-Norm Point on a Convex Polytope: Wolfe's Combinatorial Algorithm is Exponential

Student-Run Applied & Math Seminar

Speaker: Jamie Haddock, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~jhaddock/
Location: 2112 MSB
Start time: Thu, Mar 15 2018, 12:10PM

The complexity of Philip Wolfe's method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. The method is important because it is used as a subroutine for one of the most practical algorithms for submodular function minimization. We present the first example that Wolfe's method takes exponential time. Additionally, we improve previous results to show that linear programming reduces in strongly-polynomial time to the minimum norm point problem over a simplex.

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