IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4857-d1293190.html
   My bibliography  Save this article

A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems

Author

Listed:
  • Kin Keung Lai

    (International Business School, Shaanxi Normal University, Xi’an 710048, China)

  • Shashi Kant Mishra

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

  • Bhagwat Ram

    (Centre for Digital Transformation, Indian Institute of Management Ahmedabad, Vastrapur, Ahmedabad 380015, India)

  • Ravina Sharma

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

Abstract

Quantum computing is an emerging field that has had a significant impact on optimization. Among the diverse quantum algorithms, quantum gradient descent has become a prominent technique for solving unconstrained optimization (UO) problems. In this paper, we propose a quantum spectral Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) approach. The technique is considered as a generalization of the spectral PRP method which employs a q -gradient that approximates the classical gradient with quadratically better dependence on the quantum variable q . Additionally, the proposed method reduces to the classical variant as the quantum variable q approaches closer to 1. The quantum search direction always satisfies the sufficient descent condition and does not depend on any line search (LS). This approach is globally convergent with the standard Wolfe conditions without any convexity assumption. Numerical experiments are conducted and compared with the existing approach to demonstrate the improvement of the proposed strategy.

Suggested Citation

  • Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram & Ravina Sharma, 2023. "A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems," Mathematics, MDPI, vol. 11(23), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4857-:d:1293190
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4857/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4857/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Y.H. Dai & Y. Yuan, 2001. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 33-47, March.
    2. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram, 2020. "On q -Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    3. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
    4. Songhai Deng & Zhong Wan & Xiaohong Chen, 2013. "An Improved Spectral Conjugate Gradient Algorithm for Nonconvex Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 820-842, June.
    5. Awwal, Aliyu Muhammed & Kumam, Poom & Abubakar, Auwal Bala, 2019. "Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    6. Gouvêa, Érica J.C. & Regis, Rommel G. & Soterroni, Aline C. & Scarabello, Marluce C. & Ramos, Fernando M., 2016. "Global optimization using q-gradients," European Journal of Operational Research, Elsevier, vol. 251(3), pages 727-738.
    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. Kin Keung Lai & Shashi Kant Mishra & Ravina Sharma & Manjari Sharma & Bhagwat Ram, 2023. "A Modified q-BFGS Algorithm for Unconstrained Optimization," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    2. Elena Tovbis & Vladimir Krutikov & Predrag Stanimirović & Vladimir Meshechkin & Aleksey Popov & Lev Kazakovtsev, 2023. "A Family of Multi-Step Subgradient Minimization Methods," Mathematics, MDPI, vol. 11(10), pages 1-24, May.
    3. Hiroyuki Sakai & Hideaki Iiduka, 2020. "Hybrid Riemannian conjugate gradient methods with global convergence properties," Computational Optimization and Applications, Springer, vol. 77(3), pages 811-830, December.
    4. Dalton, Gordon & Bardócz, Tamás & Blanch, Mike & Campbell, David & Johnson, Kate & Lawrence, Gareth & Lilas, Theodore & Friis-Madsen, Erik & Neumann, Frank & Nikitas, Nikitakos & Ortega, Saul Torres &, 2019. "Feasibility of investment in Blue Growth multiple-use of space and multi-use platform projects; results of a novel assessment approach and case studies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 107(C), pages 338-359.
    5. Bayramov, Vugar & Abbas, Gulnara, 2017. "Oil shock in the Caspian Basin: Diversification policy and subsidized economies," Resources Policy, Elsevier, vol. 54(C), pages 149-156.
    6. Zhang, Xingping & Liang, Yanni & Yu, Enhai & Rao, Rao & Xie, Jian, 2017. "Review of electric vehicle policies in China: Content summary and effect analysis," Renewable and Sustainable Energy Reviews, Elsevier, vol. 70(C), pages 698-714.
    7. Serge Gratton & Vincent Malmedy & Philippe Toint, 2012. "Using approximate secant equations in limited memory methods for multilevel unconstrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 967-979, April.
    8. Priester, C. Robert & Melbourne-Thomas, Jessica & Klocker, Andreas & Corney, Stuart, 2017. "Abrupt transitions in dynamics of a NPZD model across Southern Ocean fronts," Ecological Modelling, Elsevier, vol. 359(C), pages 372-382.
    9. Loeb, Benjamin & Kockelman, Kara M., 2019. "Fleet performance and cost evaluation of a shared autonomous electric vehicle (SAEV) fleet: A case study for Austin, Texas," Transportation Research Part A: Policy and Practice, Elsevier, vol. 121(C), pages 374-385.
    10. Ahmad M. Alshamrani & Adel Fahad Alrasheedi & Khalid Abdulaziz Alnowibet & Salem Mahdi & Ali Wagdy Mohamed, 2022. "A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization Problems," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    11. Rogeau, A. & Girard, R. & Kariniotakis, G., 2017. "A generic GIS-based method for small Pumped Hydro Energy Storage (PHES) potential evaluation at large scale," Applied Energy, Elsevier, vol. 197(C), pages 241-253.
    12. Li, Qing'an & Maeda, Takao & Kamada, Yasunari & Hiromori, Yuto, 2018. "Investigation of wake characteristic of a 30 kW rated power Horizontal Axis Wind Turbine with wake model and field measurement," Applied Energy, Elsevier, vol. 225(C), pages 1190-1204.
    13. Gonglin Yuan & Zhou Sheng & Wenjie Liu, 2016. "The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-15, October.
    14. B. Sellami & Y. Chaib, 2016. "A new family of globally convergent conjugate gradient methods," Annals of Operations Research, Springer, vol. 241(1), pages 497-513, June.
    15. Neculai Andrei, 2013. "Another Conjugate Gradient Algorithm with Guaranteed Descent and Conjugacy Conditions for Large-scale Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 159-182, October.
    16. N. Andrei, 2009. "Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 249-264, May.
    17. Poulsen, Thomas & Lema, Rasmus, 2017. "Is the supply chain ready for the green transformation? The case of offshore wind logistics," Renewable and Sustainable Energy Reviews, Elsevier, vol. 73(C), pages 758-771.
    18. Rabiu Bashir Yunus & Nooraini Zainuddin & Hanita Daud & Ramani Kannan & Samsul Ariffin Abdul Karim & Mahmoud Muhammad Yahaya, 2023. "A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    19. Milena Keskin, 2016. "Trendy rozwojowe franchisingu w Polsce i Europie / Franchising development trends in Poland and Europe," International Economics, University of Lodz, Faculty of Economics and Sociology, issue 13, pages 53-70, March.
    20. Hiroyuki Sakai & Hideaki Iiduka, 2021. "Sufficient Descent Riemannian Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 130-150, July.

    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:gam:jmathe:v:11:y:2023:i:23:p:4857-:d:1293190. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.