A generalized proximal-point method for convex optimization problems in Hilbert spaces. (3rd October 2017)

• Record Type: Journal Article
• Authors: Kanzow, Christian; Steck, Daniel
• Is Part Of: Optimization. Volume 66:Number 10(2017)
• Page Start: 1667
• Page End: 1676
• Publication Date: 2017-10-03
• Subjects: Generalized proximal-point method -- Tikhonov regularization -- global convergence -- augmented Lagrangian method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1349127
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: We deal with a generalization of the proximal-point method and the closely related Tikhonov regularization method for convex optimization problems. The prime motivation behind this is the well-known connection between the classical proximal-point and augmented Lagrangian methods, and the emergence of modified augmented Lagrangian methods in recent years. Our discussion includes a formal proof of a corresponding connection between the generalized proximal-point method and the modified augmented Lagrange approach in infinite dimensions. Several examples and counterexamples illustrate the convergence properties of the generalized proximal-point method and indicate that the corresponding assumptions are sharp.