Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems

Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems
Author :
Publisher : Logos Verlag Berlin GmbH
Total Pages : 255
Release :
ISBN-10 : 9783832528904
ISBN-13 : 3832528903
Rating : 4/5 (903 Downloads)

Book Synopsis Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems by : Nils Langenberg

Download or read book Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems written by Nils Langenberg and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several regularization methods for variational inequalities and fixed point problems are studied. Known convergence results especially require some kind of monotonicity of the problem data as well as, especially for Bregman-function-based algorithms, some additional assumption known as the cutting plane property. Unfortunately, these assumptions may be considered as rather restrictive e.g. in the framework of Nash equilibrium problems. This motivates the development of convergence results under weaker hypotheses which constitute the major subject of the present book. Studied methods include the Bregman-function-based Proximal Point Algorithm (BPPA), Cohen's Auxiliary Problem Principle and an extragradient algorithm.Moreover, this work also contains the first numerical comparison of stopping criteria in the framework of the BPPA. Although such conditions are the subject of theoretical investigations frequently, their numerical effectiveness and a deducible preference were still unknown. This gives rise to the necessity of the presented numerical experiments.


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