Computational Optimization and Applications

, Volume 54, Issue 1, pp 77–91 | Cite as

An acceleration scheme for cyclic subgradient projections method



An algorithm for solving convex feasibility problem for a finite family of convex sets is considered. The acceleration scheme of De Pierro (em Methodos de projeção para a resolução de sistemas gerais de equações algébricas lineares. Thesis (tese de Doutoramento), Instituto de Matemática da UFRJ, Cidade Universitária, Rio de Janeiro, Brasil, 1981), which is designed for simultaneous algorithms, is used in the algorithm to speed up the fully sequential cyclic subgradient projections method. A convergence proof is presented. The advantage of using this strategy is demonstrated with some examples.


Iterative methods Convex feasibility problem Cyclic subgradient projections method 



The author thanks Professors Yair Censor and Tommy Elfving for their valuable advices and discussions. In particular, the idea to accelerate ART was communicated to us by Professor Censor and was further discussed with Professor Andrzej Cegielski. We also wish to thank three anonymous referees for constructive criticism and helpful suggestions which improved our paper.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsIran University of Science and TechnologyTehranIran

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