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

Kin Keung Lai, Shashi Kant Mishra, Bhagwat Ram () and Ravina Sharma
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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

Mathematics, 2023, vol. 11, issue 23, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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