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Convergence analysis of proximal-like methods for variational inequalities and fixed point problems. Applications to the Nash equilibrium problem

Nils Langenberg

ISBN 978-3-8325-2890-4
256 pages, year of publication: 2011
price: 41.00 €
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.

Keywords:
  • variational inequalities
  • fixed point problems
  • Nash equilibrium problems
  • proximal-like methods
  • Bregman functions

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41.00 €