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Radiant Separation Theorems and Minimum-Type Subdifferentials of Calm Functions

Author

Listed:
  • A. Sheykhi

    (Shahid Bahonar University of Kerman)

  • A. R. Doagooei

    (Shahid Bahonar University of Kerman)

Abstract

Applying minimum-type functions and plus-cogauges, we construct a closed, convex cone in order to separate a boundary point of a radiant set from its interior. Abstract convexity of positively homogeneous functions is studied as well. Since a locally Lipschitz function is degree-one calm, the class of degree-one calm functions is large. We study degree-one calm functions and investigate how these functions can be generated by a class of min-type functions. Then, we derive a method to find an element of the subdifferential of a non-negative, lower semicontinuous and degree-one calm function with respect to the class of min-type functions.

Suggested Citation

  • A. Sheykhi & A. R. Doagooei, 2017. "Radiant Separation Theorems and Minimum-Type Subdifferentials of Calm Functions," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 693-711, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1132-1
    DOI: 10.1007/s10957-017-1132-1
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    References listed on IDEAS

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    1. Adil Bagirov & Julien Ugon & Dean Webb & Gurkan Ozturk & Refail Kasimbeyli, 2013. "A novel piecewise linear classifier based on polyhedral conic and max–min separabilities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 3-24, April.
    2. Alberto Zaffaroni, 2004. "Is every radiant function the sum of quasiconvex functions?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 221-233, June.
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