We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality framework extends convergence results for the Kacanov scheme to a broader class of problems.

翻译：我们将对偶理论应用于离散化凸极小化问题，从而获得给定离散函数与精确离散极小化器之间距离的可计算保证上界。此外，我们证明了离散对偶框架可将Kacanov格式的收敛性结果推广至更广泛的问题类别。