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

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–P...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 23; p. 4857
Main Authors Lai, Kin Keung, Mishra, Shashi Kant, Ram, Bhagwat, Sharma, Ravina
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2023
Subjects
Algorithms
Approximation
Conjugate gradient method
Convexity
global convergence
Literature reviews
Methods
Optimization
quantum calculus
Quantum computing
unconstrained optimization
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11234857