The Euclidean distance degree of Fermat hypersurfaces

摘要

Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a piecewise polynomial whose pieces are defined by subtle congruence conditions. (C) 2016 Elsevier Ltd. All rights reserved.