facial distance

Calculus of the facial distance

Categories Convex and Nonsmooth Optimization, Polyhedra Tags , ,

We develop a few calculus rules to compute or lower bound the facial distance of a polytope. We illustrate our calculus rules on various popular polytopes. In particular, we provide a lower bound on the facial distance of the Birkhoff polytope. CitationWorking paper. Tepper School of Business. Carnegie Mellon UniversityArticleDownload View PDF

The condition of a function relative to a polytope

Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , ,

The condition number of a smooth convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function. In particular, the condition number of a quadratic convex function is precisely the square of the diameter-to-width ratio of a canonical ellipsoid associated to the function. Furthermore, the … Read more