Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms

Abstract. The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions – computing the size of projections of high dimensional polytopes and estimating the norms of random matrices and their inverses.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Roman Vershynin
• Keywords: Asymptotic Convex Geometry, CORR 2007, Education, Linear Programming, Simplex Method