A priori stopping rule for an iterative Bregman method for optimal control problems. (4th March 2018)

• Record Type: Journal Article
• Authors: Pörner, Frank
• Is Part Of: Optimization methods and software. Volume 33:Number 2(2018)
• Page Start: 249
• Page End: 267
• Publication Date: 2018-03-04
• Subjects: source condition -- Bregman distance -- noise error estimates -- stopping rule; 49M15 -- 49N45 -- 65K10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2017.1300661
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this article we continue our investigation of the iterative regularization method for optimization problems based on Bregman distances. The optimization problems are subject to pointwise inequality constraints in . We provide an estimate for the noise error for perturbed data, which can be used to construct an a priori stopping rule. Furthermore we show how to implement our method with a semi-smooth Newton method using finite elements and present numerical results for the stopping rule.