Accuracy Certificates for Computational Problems with Convex Structure

Authors:
Arkadi Nemirovski;Shmuel Onn;Uriel G. Rothblum
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;Faculty of Industrial Engineering and Management, Technion---Israel Institute of Technology, Technion City, Haifa 32000, Israel;Faculty of Industrial Engineering and Management, Technion---Israel Institute of Technology, Technion City, Haifa 32000, Israel
Venue:
Mathematics of Operations Research
Year:
2010

Citing 9
Cited 0

Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Mathematical Programming: Series A and B
New variants of bundle methods

Mathematical Programming: Series A and B
Location of the Maximum on Unimodal Surfaces

Journal of the ACM (JACM)
Lectures on modern convex optimization: analysis, algorithms, and engineering applications

Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Convex Optimization

Convex Optimization
Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems

SIAM Journal on Optimization
Non-euclidean restricted memory level method for large-scale convex optimization

Mathematical Programming: Series A and B
Smooth minimization of non-smooth functions

Mathematical Programming: Series A and B
An old linear programming algorithm runs in polynomial time

SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

The goal of this 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 significant increase of the computational effort. Further, we show that (computable) certificates exist for any algorithm that is capable of producing solutions of guaranteed accuracy.