Accuracy Certificates for Computational Problems with Convex Structure

The goal of the current paper is to introduce the notion of certificates which verify the accuracy of solutions of computational problems with convex structure; such problems include minimizing convex functions, variational inequalities with monotone operators, computing saddle points of convex-concave functions and solving convex Nash equilibrium problems. We demonstrate how the implementation of the Ellipsoid method and other cutting plane algorithms can be augmented with the computation of such certificates without essential increase of the computational effort. Further, we show that (computable) certificates exist whenever an algorithm is capable to produce solutions of guaranteed accuracy. Key words: convexity, certificates, computation in convex structures, convex minimization, variational inequalities, saddle points, convex Nash equilibrium 1 Supported in part by NSF grant DMI 0619977 2 Supported in part by a grant from ISF - the Israel Science Foundation, by a VPR grant a...

• Type: Journal
• Year: 2010
• Where: MOR
• Authors: Arkadi Nemirovski, Shmuel Onn, Uriel G. Rothblum
• Keywords: Convex Nash Equilibrium, Convex Structures, Israel Science Foundation, MOR 2010