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Exterior point simplex-type algorithms for linear and network optimization problems

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Abstract

Two decades of research led to the development of a number of efficient algorithms that can be classified as exterior point simplex-type. This type of algorithms can cross over the infeasible region of the primal (dual) problem and find an optimal solution reducing the number of iterations needed. The main idea of exterior point simplex-type algorithms is to compute two paths/flows. Primal (dual) exterior point simplex-type algorithms compute one path/flow which is basic but not always primal (dual) feasible and the other is primal (dual) feasible but not always basic. The aim of this paper is to explain to the general OR audience, for the first time, the developments in exterior point simplex-type algorithms for linear and network optimization problems, over the recent years. We also present other approaches that, in a similar way, do not preserve primal or dual feasibility at each iteration such as the monotonic build-up Simplex algorithms and the criss-cross methods.

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Acknowledgments

It is with sorrow that we note that, during the preparation of this paper, the first author Prof. Konstantinos Paparrizos, suddenly and unexpectedly passed away. Prof. Konstantinos Paparrizos was a well respected and loved colleague for the Operations Research community, at the international level, for his excellent scientific activity and sincerity. He was a very active researcher and he had successfully stimulated many young scientists. The main research results of his career, together with contributions from the other two co-authors who were honored to be supervised by him during their Ph.D. studies, are presented in this paper, which we dedicate to his memory. Finally, we would also like to express our gratitude to the referees, whose their instructive comments greatly improved the quality of the paper.

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  1. Department of Applied Informatics, School of Information Sciences, University of Macedonia, 156 Egnatias Str., 54636, Thessaloníki, Greece

    Konstantinos Paparrizos, Nikolaos Samaras & Angelo Sifaleras

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  1. Konstantinos Paparrizos
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Paparrizos, K., Samaras, N. & Sifaleras, A. Exterior point simplex-type algorithms for linear and network optimization problems. Ann Oper Res 229, 607–633 (2015). https://doi.org/10.1007/s10479-014-1769-1

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