Global convergence of some modified PRP nonlinear conjugate gradient methods

Dai, Zhifeng; Tian, Boshi

doi:10.1007/s11590-010-0224-8

Cited by 26 publications

(14 citation statements)

References 17 publications

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“…To solve this problem, there have been many algorithms such as DPRP (Polak and Ribiere, 1969), NMPRP (Dai et al, 2000), DMPRP (Yu, 2007) and PRP-DC (Yuan, 2009) corrected for PRP, and analyzed the convergence (Andrei, 2011;Zhang, Zhou, and Li, 2006). Recently, Zhang et al (Dai and Tian, 2011) also proposed a modified PRP method satisfies sufficient descent, numerical results show that this method are global convergence both on uniformly convex functions and general nonlinear functions. Inspired by the thought of literature (Dai and Tian, 2011), this paper presents a modified PRP conjugate gradient (MPRPCG) algorithm, which uses learning algorithm based on MPRPCG to modify the five sets of parameters in the QNN model: quantum rotation gate phase θi , hidden layer connection weights argument βij , hidden layer activity value argument γij , threshold γij, and the output layer connection weights wjk.…”

Section: Learning Algorithms and Global Convergence Analysismentioning

confidence: 99%

Small Time-Scale Network Tidal Water Level Forecasting Based on Quantum Neural Network

Zhao

Wang

Guo

2015

Journal of Coastal Research

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Zhao, K.; Wang, H., and Guo, T., 2015. Small time-scale network traffic prediction on the basis of Quantum Neural This paper proposed a quantum neural network model consist of quantum bit, universal quantum gates and quantum weighted, gave the learning algorithm based on improved PRP conjugate gradient, in order to improve the convergence speed of the network and the network performance, and further proved the global convergence of the algorithm in theory. Compared with the existing localized support vector machine (SVM) regression and flexible neural tree model, the QNN model proposed in this paper have a higher prediction precision and low computational complexity for small scale tidal water level prediction, its convergence speed and robustness are better than BP network and quantum weighted neural network.

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Section: Learning Algorithms and Global Convergence Analysismentioning

confidence: 99%

Small Time-Scale Network Tidal Water Level Forecasting Based on Quantum Neural Network

Zhao

Wang

Guo

2015

Journal of Coastal Research

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“…Furthermore, if β k in (6) is specified by an existing conjugate gradient formula, we obtain the corresponding modified conjugate gradient method [9,10,22,[32][33][34][35]. Recently, researchers [7,[22][23][24][25]30] paid special attention to hybridize the above two approaches.…”

Section: Introductionmentioning

confidence: 99%

A limited memory descent Perry conjugate gradient method

Livieris

Pintelas

2015

Optim Lett

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In this work, we present a new limited memory conjugate gradient method which is based on the study of Perry's method. An attractive property of the proposed method is that it corrects the loss of orthogonality that can occur in ill-conditioned optimization problems, which can decelerate the convergence of the method. Moreover, an additional advantage is that the memory is only used to monitor the orthogonality relatively cheaply; and when orthogonality is lost, the memory is used to generate a new orthogonal search direction. Under mild conditions, we establish the global convergence of the proposed method provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate the efficiency and robustness of the proposed method.

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“…Zhang et al [11]propose a modified Polak-Ribiere-Polyak (PRP) conjugate gradient method with Armijo-type line search, then gain the global convergence property with sufficient descent direction. Dai and Tian [12] take a little modification to Zhang's method such that the modified method retain sufficient descent property. Without requirement of the positive lower bound of the step size, they prove that the proposed methods are globally convergent.…”

Section: Introductionmentioning

confidence: 99%