- Rounding on the standard simplex: regular grids for global optimization Immanuel M. Bomze (immanuel.bomzeunivie.ac.at) Stefan Gollowitzer (stefan.gollowitzerunivie.ac.at) E. Alper Yildirim (alperyildirimku.edu.tr) Abstract: Given a point on the standard simplex, we calculate a proximal point on the regular grid which is closest with respect to any norm in a large class, including all $\ell^p$-norms for $p\ge 1$. We show that the minimal $\ell^p$-distance to the regular grid on the standard simplex can exceed one, even for very fine mesh sizes in high dimensions. Furthermore, for $p=1$, the maximum minimal distance approaches the $\ell^1$-diameter of the standard simplex. We also put our results into perspective to the literature on approximating global optimization problems over the standard simplex by means of the regular grid. Keywords: approximation; maximin distance; proximal point Category 1: Global Optimization (Theory ) Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Download: [PDF]Entry Submitted: 09/17/2013Entry Accepted: 09/17/2013Entry Last Modified: 10/19/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.