Linear Programming 3: Polytopes, cubes, and cross-polytopes скачать в хорошем качестве

Linear Programming 3: Polytopes, cubes, and cross-polytopes

Linear Programming 3: Polytopes, cubes, and cross-polytopes Abstract: We give a very high-level introduction to polytopes. We mention the main theorem of polytopes: that polytopes defined as (bounded) intersections of half-spaces are the same objects as polytopes defined as convex hulls of a finite number of points. We explain how cubes have an exponential number of vertices in terms of the number of faces, and how cross-polytopes have an exponential number of faces in terms of the number of vertices. Therefore, for general polytopes, we do not expect there to be polynomial time algorithms for translating from a face description to a vertex description, or vice-versa. This video accompanies the class "Linear Programming and Network Flows" at Colorado State University https://www.math.colostate.edu/~adams... We are following the book "Understanding and Using Linear Programming" by Jiří Matoušek and Bernd Gärtner https://link.springer.com/book/10.100... Our course notes are available at https://www.math.colostate.edu/~adams...