We introduce a continuous analogue of the Hirsch conjecture and a discrete analogue of the result of Dedieu, Malajovich and Shub. We prove a continuous analogue of the result of Holt and Klee, namely, we construct a family of polytopes which attain the conjectured order of the largest total curvature.
Citation
AdvOL-Report #2006/09 Advanced Optimization Laboratory, McMaster University, Hamilton, Ontario, Canada, August 2006.