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Cone asymptotes of convex sets

  • V. Soltan [1]
    1. [1] George Mason University

      George Mason University

      Estados Unidos

  • Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 36, Nº 1, 2021, págs. 81-98
  • Idioma: inglés
  • DOI: 10.17398/2605-5686.36.1.81
  • Enlaces
  • Resumen
    • Based on the notion of plane asymptote, we introduce the new concept of cone asymptote of a set in the n-dimensional Euclidean space. We discuss the existence and describe some families of cone asymptotes.

  • Referencias bibliográficas
    • [1] A. Auslender, M. Teboulle, “Asymptotic Cones and Functions in Optimization and Variational Inequalities”, Springer-Verlag, New York, 2003.
    • [2] D. Gale, V. Klee, Continuous convex sets, Math. Scand. 7 (1959), 379 – 391.
    • [3] P. Goossens, Hyperbolic sets and asymptotes, J. Math. Anal. Appl. 116 (1986), 604 – 618.
    • [4] V. Klee, Asymptotes and projections of convex sets, Math. Scand. 8 (1960), 356 – 362.
    • [5] V.L. Klee, Asymptotes of convex bodies, Math. Scand. 20 (1967), 89 – 90.
    • [6] J. Lawrence, V. Soltan, On unions and intersections of nested families of cones, Beitr. Algebra Geom. 57 (2016), 655 – 665.
    • [7] J.E. Martı́nez-Legaz, D. Noll, W. Sosa, Minimization of quadratic functions on convex sets without asymptotes, J. Convex Anal. 25 (2018),...
    • [8] J.E. Martı́nez-Legaz, D. Noll, W. Sosa, Non-polyhedral extensions of the Frank and Wolfe theorem, in “Splitting Algorithms, Modern Operator...
    • [9] V. Soltan, Asymptotic planes and closedness conditions for linear images and vector sums of sets, J. Convex Anal. 25 (2018), 1183 – 1196.
    • [10] V. Soltan, “Lectures on Convex Sets”, Second edition, World Scientific, Hackensack, NJ, 2020.
    • [11] V. Soltan, On M-decomposable sets, J. Math. Anal. Appl. 485 (2020), 123816, 15 pp.

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