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Workshop

Decomposition Polyhedra of Piecewise Linear Functions

  • Marie Brandenburg (Ruhr-Universität Bochum)
E1 05 (Leibniz-Saal)

Abstract

It is well-known that every continuous piecewise linear function can be written as the difference of two convex piecewise linear functions. For applications in optimization and neural network theory, it is crucial to find decompositions where the convex functions have as few linear pieces as possible. But how can we find such a minimal decomposition, and how small can a minimal decomposition be?

Under certain assumptions, we can describe the space of all convex decompositions as a polyhedron. In this talk, we will discuss properties of these polyhedra, and how this point of view can contribute to finding a minimal decomposition.

This talk is based on joint work with Moritz Grillo and Christoph Hertrich.

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Thomas Kahle

Otto-von-Guericke-Universität

Bernd Sturmfels

Max-Planck-Institut für Mathematik in den Naturwissenschaften

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