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Novel Constructions for Closed Convex Cones Through Inequalities and Support Functions

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  • Ching-Yu Yang

    (National Taiwan Normal University)

  • Yu-Lin Chang

    (National Taiwan Normal University)

  • Chu-Chin Hu

    (National Taiwan Normal University)

  • Jein-Shan Chen

    (National Taiwan Normal University)

Abstract

Two novel ways to generate closed convex cones, the main ingredient of conic optimization, are proposed in this study. The first way is constructing closed convex cones via inequalities, whereas the second one is through support functions. The contribution of this article is twofold. One is opening up new ideas for looking into structures of closed convex cones. The other one is providing novel approaches and mediums for investigating conic optimization.

Suggested Citation

  • Ching-Yu Yang & Yu-Lin Chang & Chu-Chin Hu & Jein-Shan Chen, 2025. "Novel Constructions for Closed Convex Cones Through Inequalities and Support Functions," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-34, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02654-z
    DOI: 10.1007/s10957-025-02654-z
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    References listed on IDEAS

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    1. S. Németh & G. Zhang, 2015. "Extended Lorentz cones and mixed complementarity problems," Journal of Global Optimization, Springer, vol. 62(3), pages 443-457, July.
    2. Jein-Shan Chen, 2007. "On Some Ncp-Functions Based On The Generalized Fischer–Burmeister Function," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 401-420.
    3. O. P. Ferreira & S. Z. Németh, 2018. "How to project onto extended second order cones," Journal of Global Optimization, Springer, vol. 70(4), pages 707-718, April.
    4. Sándor Zoltán Németh & Guohan Zhang, 2016. "Extended Lorentz Cones and Variational Inequalities on Cylinders," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 756-768, March.
    5. Sándor Zoltán Németh & Lianghai Xiao, 2018. "Linear Complementarity Problems on Extended Second Order Cones," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 269-288, February.
    6. Le Hien, 2015. "Differential properties of Euclidean projection onto power cone," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 265-284, December.
    7. François Glineur, 2001. "Proving Strong Duality for Geometric Optimization Using a Conic Formulation," Annals of Operations Research, Springer, vol. 105(1), pages 155-184, July.
    8. Yingchao Gao & Sándor Zoltán Németh & Roman Sznajder, 2022. "The Monotone Extended Second-Order Cone and Mixed Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 381-407, June.
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