Guaranteed upper bounds for iteration errors and modified Kacanov schemes via discrete duality

TL;DR

This paper develops a duality-based approach to provide guaranteed upper bounds on iteration errors in convex minimization problems and extends convergence analysis for the Kacanov scheme to more problem classes.

Contribution

It introduces a discrete duality framework that yields computable error bounds and broadens convergence results for the Kacanov scheme.

Findings

Guaranteed upper bounds for discrete minimizer errors

Extended convergence results for Kacanov scheme

Applicability to a broader class of convex problems

Abstract

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.