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

Abstract: 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.

game theorymachine learningmathematical softwarecomputer science theorycombinatoricsoptimization and control

Audience: researchers in the topic

Mixed Integer Programming Workshop 2021

Series comments: The 18th Mixed Integer Programming Workshop will be held online on May 24-27, 2021.

It will feature 21 distinguished invited speakers covering most aspects of Mathematical Optimization, an interactive, gamified MIP student poster session with 50 posters, and a casual business meeting.

Registration is free of charge. Register here: fico.zoom.us/webinar/register/2416186463858/WN_DVLhGOToQkKyvKYPiA4cQw

Find the website of MIP2021 at sites.google.com/view/mipworkshop2021/.