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On Notations for Conic Hulls and Related Considerations on Tangent Cones

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  • Giorgio Giorgi

Abstract

We propose two di erent notations for cones generated by a set and for convex cones generated by a set, usually denoted by a same notation. We make some remarks on the Bouligand tangent cone and on the Clarke tangent cone for star-shaped sets and for locally convex sets. We give some applications of these remarks to a di erentiable optimization problem with an abstract constraint.

Suggested Citation

  • Giorgio Giorgi, 2021. "On Notations for Conic Hulls and Related Considerations on Tangent Cones," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 13(3), pages 1-13, June.
    • Handle: RePEc:ibn:jmrjnl:v:13:y:2021:i:3:p:13
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    References listed on IDEAS

    as
    1. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    2. Byron J. T. Morgan, 1989. "Introduction to Optimization," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 152(2), pages 254-255, March.
    3. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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