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On Lagrange duality theory for dynamics vaccination games

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Abstract

The authors study an infinite dimensional duality theory finalized to obtain the existence of a strong duality between a convex optimization problem connected with the management of vaccinations and its Lagrange dual. Specifically, the authors show the solvability of a dual problem using as basic tool an hypothesis known as Assumption S. Roughly speaking, it requires to show that a particular limit is nonnegative. This technique improves the previous strong duality results that need the nonemptyness of the interior of the convex ordering cone. The authors use the duality theory to analyze the dynamic vaccination game in order to obtain the existence of the Lagrange multipliers related to the problem and to better comprehend the meaning of the problem.

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Acknowledgements

We wish to warmly thank Professor A. Maugeri for the proficuous discussions. The second author is partially supported by the Ministry of Education and Science of the Russian Federation (Agreement number N. 02.03.21.0008).

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Authors and Affiliations

  1. Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, via Cinthia, 80126, Naples, Italy

    Annamaria Barbagallo

  2. Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 6, S.M. Nikolskii Institute of Mathematics at RUDN University, 117198, Moscow, Russia

    Maria Alessandra Ragusa

Authors
  1. Annamaria Barbagallo
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  2. Maria Alessandra Ragusa
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Correspondence to Annamaria Barbagallo.

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Barbagallo, A., Ragusa, M.A. On Lagrange duality theory for dynamics vaccination games. Ricerche mat 67, 969–982 (2018). https://doi.org/10.1007/s11587-018-0414-8

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  • DOI: https://doi.org/10.1007/s11587-018-0414-8

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