IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v13y2021i3p13.html
   My bibliography  Save this article

On Notations for Conic Hulls and Related Considerations on Tangent Cones

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/download/0/0/45116/47801
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/0/45116
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marius Durea & Radu Strugariu & Christiane Tammer, 2013. "Scalarization in Geometric and Functional Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 635-655, December.
    2. Thai Chuong, 2013. "Newton-like methods for efficient solutions in vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 495-516, April.
    3. Boualem Alleche & Vicenţiu D. Rădulescu, 2017. "Further on Set-Valued Equilibrium Problems and Applications to Browder Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 39-58, October.
    4. Sorin-Mihai Grad & Felipe Lara, 2022. "An extension of the proximal point algorithm beyond convexity," Journal of Global Optimization, Springer, vol. 82(2), pages 313-329, February.
    5. Alberto Del Pia & Robert Hildebrand & Robert Weismantel & Kevin Zemmer, 2016. "Minimizing Cubic and Homogeneous Polynomials over Integers in the Plane," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 511-530, May.
    6. A. Kabgani & F. Lara, 2023. "Semistrictly and neatly quasiconvex programming using lower global subdifferentials," Journal of Global Optimization, Springer, vol. 86(4), pages 845-865, August.
    7. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    8. Li, Ruihai & Chan, Ya-Lan & Chang, Chun-Tao & Cárdenas-Barrón, Leopoldo Eduardo, 2017. "Pricing and lot-sizing policies for perishable products with advance-cash-credit payments by a discounted cash-flow analysis," International Journal of Production Economics, Elsevier, vol. 193(C), pages 578-589.
    9. Edgardo Brigatti & Felipe Macias & Max O. Souza & Jorge P. Zubelli, 2015. "A Hedged Monte Carlo Approach to Real Option Pricing," Papers 1509.03577, arXiv.org.
    10. R. Cambini & R. Riccardi & D. Scopelliti, 2023. "Solving linear multiplicative programs via branch-and-bound: a computational experience," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.
    11. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.
    12. Al-Amin Khan, Md. & Shaikh, Ali Akbar & Konstantaras, Ioannis & Bhunia, Asoke Kumar & Cárdenas-Barrón, Leopoldo Eduardo, 2020. "Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price," International Journal of Production Economics, Elsevier, vol. 230(C).
    13. Dye, Chung-Yuan & Yang, Chih-Te & Kung, Fang-Cheng, 2014. "A note on “Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime”," European Journal of Operational Research, Elsevier, vol. 239(3), pages 868-871.
    14. Delle Site, Paolo & Kilani, Karim & Gatta, Valerio & Marcucci, Edoardo & de Palma, André, 2019. "Estimation of consistent Logit and Probit models using best, worst and best–worst choices," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 87-106.
    15. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
    16. Bolte, Jérôme & Le, Tam & Pauwels, Edouard & Silveti-Falls, Antonio, 2022. "Nonsmooth Implicit Differentiation for Machine Learning and Optimization," TSE Working Papers 22-1314, Toulouse School of Economics (TSE).
    17. A. Iusem & F. Lara, 2022. "Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 443-461, June.
    18. Md. Sujan Miah & Md. Mominul Islam & Mahmudul Hasan & Abu Hashan Md. Mashud & Dipa Roy & Shib Sankar Sana, 2021. "A Discount Technique-Based Inventory Management on Electronics Products Supply Chain," JRFM, MDPI, vol. 14(9), pages 1-16, August.
    19. Khushboo & C. S. Lalitha, 2018. "Scalarizations for a unified vector optimization problem based on order representing and order preserving properties," Journal of Global Optimization, Springer, vol. 70(4), pages 903-916, April.
    20. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "First-Order Conditions for C0,1 Constrained vector optimization," Economics and Quantitative Methods qf0307, Department of Economics, University of Insubria.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ibn:jmrjnl:v:13:y:2021:i:3:p:13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.