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

Lai, Kin Keung; Mishra, Shashi Kant; Ram, Bhagwat; Sharma, Ravina

doi:10.3390/math11234857

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

¹

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

²

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

³

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

^*

Author to whom correspondence should be addressed.

Mathematics 2023, 11(23), 4857; https://doi.org/10.3390/math11234857

Submission received: 22 October 2023 / Revised: 23 November 2023 / Accepted: 30 November 2023 / Published: 3 December 2023

(This article belongs to the Special Issue Advanced Optimization Methods and Applications, 2nd Edition)

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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.

Keywords: unconstrained optimization; conjugate gradient method; quantum calculus; global convergence

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MDPI and ACS Style

Lai, K.K.; Mishra, S.K.; Ram, B.; Sharma, R. A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems. Mathematics 2023, 11, 4857. https://doi.org/10.3390/math11234857

AMA Style

Lai KK, Mishra SK, Ram B, Sharma R. A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems. Mathematics. 2023; 11(23):4857. https://doi.org/10.3390/math11234857

Chicago/Turabian Style

Lai, Kin Keung, Shashi Kant Mishra, Bhagwat Ram, and Ravina Sharma. 2023. "A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems" Mathematics 11, no. 23: 4857. https://doi.org/10.3390/math11234857

APA Style

Lai, K. K., Mishra, S. K., Ram, B., & Sharma, R. (2023). A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems. Mathematics, 11(23), 4857. https://doi.org/10.3390/math11234857

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

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