Lai, K.K.; Mishra, S.K.; Ram, B.; Sharma, R. A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems. Mathematics2023, 11, 4857.
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.
Lai, K.K.; Mishra, S.K.; Ram, B.; Sharma, R. A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems. Mathematics2023, 11, 4857.
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.
Abstract
Quantum computing is an emerging field that have given a significant impact on optimization. Among the diverse quantum algorithm, the quantum gradient descent has become a prominent technique for solving unconstrained optimization problems. In this paper, we propose a quantum-spectral Polak-Ribi{\'e}re-Polyak (PRP) conjugate gradient approach. The technique is considered as a generalization of the spectral PRP method which employs a $q$-gradient that approximate the classical gradient with quadratically better dependence on the quantum variable $q$. Additionally, the proposed method reduces to the classical variant as quantum variable $q$ gets closer to $1$. The quantum search direction always satisfies the sufficient descent condition and does not depend on any line search. This approach is globally convergent with the standard Wolfe line search 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
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
