Gauss---Seidel method for multi-valued inclusions with Z mappings

  • Authors:

  • E. Allevi;A. Gnudi;I. V. Konnov;S. Schaible

  • Affiliations:

  • Department of Quantitative Methods, Brescia University, Brescia, Italy;Department of Mathematics, Statistics, Informatics and Applications, Bergamo University, Bergamo, Italy 24129;Department of System Analysis and Information Technologies, Kazan University, Kazan, Russia 420008;Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taiwan 32023

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2012

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Abstract

We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss---Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented.