IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v375y2020ics0096300320300400.html
   My bibliography  Save this article

Self-concordance and matrix monotonicity with applications to quantum entanglement problems

Author

Listed:
  • Faybusovich, Leonid
  • Zhou, Cunlu

Abstract

Let V be a Euclidean Jordan algebra and Ω be a cone of invertible squares in V. Suppose that g:R+→R is a matrix monotone function on the positive semiaxis which naturally induces a function g˜:Ω→V. We show that −g˜ is compatible (in the sense of Nesterov–Nemirovski) with the standard self-concordant barrier B(x)=−lndet(x) on Ω. As a consequence, we show that for any c ∈ Ω, the functions of the form −tr(cg˜(x))+B(x) are self-concordant on Ω. In particular, the function x↦−tr(clnx) is a self-concordant barrier function on Ω. Using these results, we apply a long-step path-following algorithm developed in [L. Faybusovich and C. Zhou Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions. Comput Optim Appl, 72(3):769-795, 2019] to a number of important optimization problems arising in quantum information theory. Results of numerical experiments and comparisons with existing methods are presented.

Suggested Citation

  • Faybusovich, Leonid & Zhou, Cunlu, 2020. "Self-concordance and matrix monotonicity with applications to quantum entanglement problems," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300400
    DOI: 10.1016/j.amc.2020.125071
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320300400
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125071?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, June.
    2. Leonid Faybusovich & Cunlu Zhou, 2019. "Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions," Computational Optimization and Applications, Springer, vol. 72(3), pages 769-795, April.
    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. Shota Takahashi & Mituhiro Fukuda & Mirai Tanaka, 2022. "New Bregman proximal type algorithms for solving DC optimization problems," Computational Optimization and Applications, Springer, vol. 83(3), pages 893-931, December.
    2. Chee-Khian Sim, 2019. "Interior point method on semi-definite linear complementarity problems using the Nesterov–Todd (NT) search direction: polynomial complexity and local convergence," Computational Optimization and Applications, Springer, vol. 74(2), pages 583-621, November.
    3. Xin Jiang & Lieven Vandenberghe, 2022. "Bregman primal–dual first-order method and application to sparse semidefinite programming," Computational Optimization and Applications, Springer, vol. 81(1), pages 127-159, January.
    4. Huiyi Cao & Kamil A. Khan, 2023. "General convex relaxations of implicit functions and inverse functions," Journal of Global Optimization, Springer, vol. 86(3), pages 545-572, July.
    5. Pavel Shcherbakov & Mingyue Ding & Ming Yuchi, 2021. "Random Sampling Many-Dimensional Sets Arising in Control," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    6. Shariat Torbaghan, Shahab & Madani, Mehdi & Sels, Peter & Virag, Ana & Le Cadre, Hélène & Kessels, Kris & Mou, Yuting, 2021. "Designing day-ahead multi-carrier markets for flexibility: Models and clearing algorithms," Applied Energy, Elsevier, vol. 285(C).
    7. Jean-Jacques Forneron, 2023. "Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models," Papers 2301.07196, arXiv.org, revised Feb 2023.
    8. Azimbek Khudoyberdiev & Shabir Ahmad & Israr Ullah & DoHyeun Kim, 2020. "An Optimization Scheme Based on Fuzzy Logic Control for Efficient Energy Consumption in Hydroponics Environment," Energies, MDPI, vol. 13(2), pages 1-27, January.
    9. David Müller & Vladimir Shikhman, 2022. "Network manipulation algorithm based on inexact alternating minimization," Computational Management Science, Springer, vol. 19(4), pages 627-664, October.
    10. Mehdi Karimi & Levent Tunçel, 2020. "Primal–Dual Interior-Point Methods for Domain-Driven Formulations," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 591-621, May.
    11. Fosgerau, Mogens & Melo, Emerson & Shum, Matthew & Sørensen, Jesper R.-V., 2021. "Some remarks on CCP-based estimators of dynamic models," Economics Letters, Elsevier, vol. 204(C).
    12. Ramon de Punder & Timo Dimitriadis & Rutger-Jan Lange, 2024. "Kullback-Leibler-based characterizations of score-driven updates," Papers 2408.02391, arXiv.org, revised Sep 2024.
    13. Pham Duy Khanh & Boris S. Mordukhovich & Vo Thanh Phat & Dat Ba Tran, 2023. "Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials," Journal of Global Optimization, Springer, vol. 86(1), pages 93-122, May.
    14. Yurii Nesterov, 2021. "Superfast Second-Order Methods for Unconstrained Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 1-30, October.
    15. Roland Hildebrand, 2021. "Optimal step length for the Newton method: case of self-concordant functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 253-279, October.
    16. Forneron, Jean-Jacques, 2024. "Detecting identification failure in moment condition models," Journal of Econometrics, Elsevier, vol. 238(1).
    17. Hadi Abbaszadehpeivasti & Etienne Klerk & Moslem Zamani, 2024. "On the Rate of Convergence of the Difference-of-Convex Algorithm (DCA)," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 475-496, July.
    18. Xiaojun Zhou & Chunna Zhao & Yaqun Huang, 2023. "A Deep Learning Optimizer Based on Grünwald–Letnikov Fractional Order Definition," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    19. David Muller & Yurii Nesterov & Vladimir Shikhman, 2021. "Dynamic pricing under nested logit demand," Papers 2101.04486, arXiv.org.
    20. Hailing Wang & Changjun Yu & Yongcun Song, 2024. "An Augmented Lagrangian Method for State Constrained Linear Parabolic Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 196-226, October.

    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:eee:apmaco:v:375:y:2020:i:c:s0096300320300400. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.