A class of improved conjugate gradient methods for nonconvex unconstrained optimization

Hu, Quan; Zhang, Hongrun; Zhou, Zhengyuan; Chen, Yu

doi:10.1002/nla.2482

Cited by 5 publications

(1 citation statement)

References 37 publications

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“…At each iteration, the search direction of the suggested method was demonstrated for the descent direction of the objective function. Hu et al [17] proposed a class of an improved CG method in the support of descent direction to solve non-convex UO problems. More pertinent contributions are available in [18][19][20][21][22] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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

Lai,

Mishra,

Ram

et al. 2023

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

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

Lai,

Mishra,

Ram

et al. 2023

Mathematics

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An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

Yuan,

Shao,

Zeng

et al. 2024

Math Methods in App Sciences

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In this work, for unconstrained optimization, we introduce an improved Dai‐Liao‐style hybrid conjugate gradient method based on the hybridization‐based self‐adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self‐adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai‐Liao‐style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods.

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An efficient hybrid conjugate gradient method with an adaptive strategy and applications in image restoration problems

Chen,

Shao,

Liu

et al. 2024

Applied Numerical Mathematics

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A class of improved conjugate gradient methods for nonconvex unconstrained optimization

Cited by 5 publications

References 37 publications

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

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

An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

An efficient hybrid conjugate gradient method with an adaptive strategy and applications in image restoration problems

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