  Accuracy certificates for convex minimization problems allow for online
verification of the accuracy of approximate solutions and provide a
theoretically valid online stopping criterion. When solving the Lagrange dual
problem, accuracy certificates produce a simple way to recover an approximate
primal solution and estimate its accuracy. In this paper, we generalize
accuracy certificates for the setting of inexact first-order oracle, including
the setting of primal and Lagrange dual pair of problems. We further propose an
explicit way to construct accuracy certificates for a large class of cutting
plane methods based on polytopes. As a by-product, we show that the considered
cutting plane methods can be efficiently used with a noisy oracle even thought
they were originally designed to be equipped with an exact oracle. Finally, we
illustrate the work of the proposed certificates in the numerical experiments
highlighting that our certificates provide a tight upper bound on the objective
residual.
