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Selected Applications of Linear Semi-Infinite Systems Theory

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Abstract

In this paper we, firstly, review the main known results on systems of an arbitrary (possibly infinite) number of weak linear inequalities posed in the Euclidean space \(\mathbb {R}^{n}\) (i.e., with n unknowns), and, secondly, show the potential power of this theoretical tool by developing in detail two significant applications, one to computational geometry: the Voronoi cells, and the other to mathematical analysis: approximate subdifferentials, recovering known results in both fields and proving new ones. In particular, this paper completes the existing theory of farthest Voronoi cells of infinite sets of sites by appealing to well-known results on linear semi-infinite systems.

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Acknowledgements

The authors wish to thank the two anonymous referees for their careful reading of the manuscript and for their valuable comments.

This research was partially supported by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF); by CONICET, Argentina, Res D No 4198/17; and by Universidad Nacional de Cuyo, Secretaría de Investigación, Internacionales y Posgrado (SIIP), Res. 3922/19-R, Cod.06/D227, Argentina.

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Authors and Affiliations

  1. Department of Mathematics, University of Alicante, Alicante, Spain

    Miguel A. Goberna

  2. Facultad de Ciencias Aplicadas a la Industria, Universidad Nacional de Cuyo, Mendoza, Argentina

    Andrea B. Ridolfi

  3. Facultad de Ciencias Económicas, Universidad Nacional de Cuyo, Mendoza, Argentina

    Andrea B. Ridolfi & Virginia N. Vera de Serio

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  1. Miguel A. Goberna
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  2. Andrea B. Ridolfi
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  3. Virginia N. Vera de Serio
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Correspondence to Miguel A. Goberna.

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Goberna, M.A., Ridolfi, A.B. & Vera de Serio, V.N. Selected Applications of Linear Semi-Infinite Systems Theory. Vietnam J. Math. 48, 439–470 (2020). https://doi.org/10.1007/s10013-020-00415-1

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