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Journal of Optimization Theory and Applications

, Volume 162, Issue 2, pp 392–404 | Cite as

A Subgradient-Like Algorithm for Solving Vector Convex Inequalities

Article

Abstract

In this paper, we propose a strongly convergent variant of Robinson’s subgradient algorithm for solving a system of vector convex inequalities in Hilbert spaces. The advantage of the proposed method is that it converges strongly, when the problem has solutions, under mild assumptions. The proposed algorithm also has the following desirable property: the sequence converges to the solution of the problem, which lies closest to the starting point and remains entirely in the intersection of three balls with radius less than the initial distance to the solution set.

Keywords

Projection methods Strong convergence Subgradient algorithm Vector convex functions 

Notes

Acknowledgements

The authors were partially supported by Project PROCAD-nf-UFG/UnB/IMPA, by Project PRONEX-CNPq-FAPERJ and by Project CAPES-MES-CUBA 226/2012 “Modelos de Otimização e Aplicações”.

The authors would like to extend their gratitude toward anonymous referees whose suggestions helped us to improve the presentation of this paper.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Universidade Federal de GoiásGoiâniaBrazil
  2. 2.Instituto de Matemática e EstatísticaUniversidade Federal de Goiás, Campus SamambaiaGoiâniaBrazil

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