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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
    5. 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.
    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)

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