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

2025/01/28 by Lars Diening, Johannes Storn, Diening, Lars +1 · 1 citation
Computer Science · Engineering · Mathematics · #35J70 #49M29 #65N22 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2501.16850

openalex publication_date 2025/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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