Displaying publications 1 - 20 of 287 in total

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  1. Wang X, Song T, Gong F, Zheng P
    Sci Rep, 2016 06 10;6:27624.
    PMID: 27283843 DOI: 10.1038/srep27624
    Neural-like computing models are versatile computing mechanisms in the field of artificial intelligence. Spiking neural P systems (SN P systems for short) are one of the recently developed spiking neural network models inspired by the way neurons communicate. The communications among neurons are essentially achieved by spikes, i. e. short electrical pulses. In terms of motivation, SN P systems fall into the third generation of neural network models. In this study, a novel variant of SN P systems, namely SN P systems with self-organization, is introduced, and the computational power of the system is investigated and evaluated. It is proved that SN P systems with self-organization are capable of computing and accept the family of sets of Turing computable natural numbers. Moreover, with 87 neurons the system can compute any Turing computable recursive function, thus achieves Turing universality. These results demonstrate promising initiatives to solve an open problem arisen by Gh Păun.
    Matched MeSH terms: Neural Networks (Computer)*
  2. Illias HA, Chai XR, Abu Bakar AH, Mokhlis H
    PLoS One, 2015;10(6):e0129363.
    PMID: 26103634 DOI: 10.1371/journal.pone.0129363
    It is important to predict the incipient fault in transformer oil accurately so that the maintenance of transformer oil can be performed correctly, reducing the cost of maintenance and minimise the error. Dissolved gas analysis (DGA) has been widely used to predict the incipient fault in power transformers. However, sometimes the existing DGA methods yield inaccurate prediction of the incipient fault in transformer oil because each method is only suitable for certain conditions. Many previous works have reported on the use of intelligence methods to predict the transformer faults. However, it is believed that the accuracy of the previously proposed methods can still be improved. Since artificial neural network (ANN) and particle swarm optimisation (PSO) techniques have never been used in the previously reported work, this work proposes a combination of ANN and various PSO techniques to predict the transformer incipient fault. The advantages of PSO are simplicity and easy implementation. The effectiveness of various PSO techniques in combination with ANN is validated by comparison with the results from the actual fault diagnosis, an existing diagnosis method and ANN alone. Comparison of the results from the proposed methods with the previously reported work was also performed to show the improvement of the proposed methods. It was found that the proposed ANN-Evolutionary PSO method yields the highest percentage of correct identification for transformer fault type than the existing diagnosis method and previously reported works.
    Matched MeSH terms: Neural Networks (Computer)*
  3. Marto A, Hajihassani M, Armaghani DJ, Mohamad ET, Makhtar AM
    ScientificWorldJournal, 2014;2014:643715.
    PMID: 25147856 DOI: 10.1155/2014/643715
    Flyrock is one of the major disturbances induced by blasting which may cause severe damage to nearby structures. This phenomenon has to be precisely predicted and subsequently controlled through the changing in the blast design to minimize potential risk of blasting. The scope of this study is to predict flyrock induced by blasting through a novel approach based on the combination of imperialist competitive algorithm (ICA) and artificial neural network (ANN). For this purpose, the parameters of 113 blasting operations were accurately recorded and flyrock distances were measured for each operation. By applying the sensitivity analysis, maximum charge per delay and powder factor were determined as the most influential parameters on flyrock. In the light of this analysis, two new empirical predictors were developed to predict flyrock distance. For a comparison purpose, a predeveloped backpropagation (BP) ANN was developed and the results were compared with those of the proposed ICA-ANN model and empirical predictors. The results clearly showed the superiority of the proposed ICA-ANN model in comparison with the proposed BP-ANN model and empirical approaches.
    Matched MeSH terms: Neural Networks (Computer)*
  4. Tunc C
    Sains Malaysiana, 2011;40:1455-1459.
    The main purpose of this paper is to introduce some new instability theorems related to certain fourth and fifth order nonlinear differential equations with a constant delay. By means of the Lyapunov-Krasovskii functional approach, we obtained two new results on the topic.
  5. Ali SS, Moinuddin M, Raza K, Adil SH
    ScientificWorldJournal, 2014;2014:850189.
    PMID: 24987745 DOI: 10.1155/2014/850189
    Radial basis function neural networks are used in a variety of applications such as pattern recognition, nonlinear identification, control and time series prediction. In this paper, the learning algorithm of radial basis function neural networks is analyzed in a feedback structure. The robustness of the learning algorithm is discussed in the presence of uncertainties that might be due to noisy perturbations at the input or to modeling mismatch. An intelligent adaptation rule is developed for the learning rate of RBFNN which gives faster convergence via an estimate of error energy while giving guarantee to the l 2 stability governed by the upper bounding via small gain theorem. Simulation results are presented to support our theoretical development.
    Matched MeSH terms: Neural Networks (Computer)*
  6. Ahmed AU, Islam MT, Ismail M, Kibria S, Arshad H
    ScientificWorldJournal, 2014;2014:253787.
    PMID: 25133214 DOI: 10.1155/2014/253787
    An artificial neural network (ANN) and affinity propagation (AP) algorithm based user categorization technique is presented. The proposed algorithm is designed for closed access femtocell network. ANN is used for user classification process and AP algorithm is used to optimize the ANN training process. AP selects the best possible training samples for faster ANN training cycle. The users are distinguished by using the difference of received signal strength in a multielement femtocell device. A previously developed directive microstrip antenna is used to configure the femtocell device. Simulation results show that, for a particular house pattern, the categorization technique without AP algorithm takes 5 indoor users and 10 outdoor users to attain an error-free operation. While integrating AP algorithm with ANN, the system takes 60% less training samples reducing the training time up to 50%. This procedure makes the femtocell more effective for closed access operation.
    Matched MeSH terms: Neural Networks (Computer)*
  7. Mohseni SA, Tan AH
    IEEE Trans Syst Man Cybern B Cybern, 2012 Dec;42(6):1645-53.
    PMID: 22665508 DOI: 10.1109/TSMCB.2012.2197610
    This paper proposes a new mixed training algorithm consisting of error backpropagation (EBP) and variable structure systems (VSSs) to optimize parameter updating of neural networks. For the optimization of the number of neurons in the hidden layer, a new term based on the output of the hidden layer is added to the cost function as a penalty term to make optimal use of hidden units related to weights corresponding to each unit in the hidden layer. VSS is used to control the dynamic model of the training process, whereas EBP attempts to minimize the cost function. In addition to the analysis of the imposed dynamics of the EBP technique, the global stability of the mixed training methodology and constraints on the design parameters are considered. The advantages of the proposed technique are guaranteed convergence, improved robustness, and lower sensitivity to initial weights of the neural network.
    Matched MeSH terms: Neural Networks (Computer)*
  8. Chan Phooi M'ng J, Mehralizadeh M
    PLoS One, 2016;11(6):e0156338.
    PMID: 27248692 DOI: 10.1371/journal.pone.0156338
    The motivation behind this research is to innovatively combine new methods like wavelet, principal component analysis (PCA), and artificial neural network (ANN) approaches to analyze trade in today's increasingly difficult and volatile financial futures markets. The main focus of this study is to facilitate forecasting by using an enhanced denoising process on market data, taken as a multivariate signal, in order to deduct the same noise from the open-high-low-close signal of a market. This research offers evidence on the predictive ability and the profitability of abnormal returns of a new hybrid forecasting model using Wavelet-PCA denoising and ANN (named WPCA-NN) on futures contracts of Hong Kong's Hang Seng futures, Japan's NIKKEI 225 futures, Singapore's MSCI futures, South Korea's KOSPI 200 futures, and Taiwan's TAIEX futures from 2005 to 2014. Using a host of technical analysis indicators consisting of RSI, MACD, MACD Signal, Stochastic Fast %K, Stochastic Slow %K, Stochastic %D, and Ultimate Oscillator, empirical results show that the annual mean returns of WPCA-NN are more than the threshold buy-and-hold for the validation, test, and evaluation periods; this is inconsistent with the traditional random walk hypothesis, which insists that mechanical rules cannot outperform the threshold buy-and-hold. The findings, however, are consistent with literature that advocates technical analysis.
    Matched MeSH terms: Neural Networks (Computer)*
  9. Abdelhaq M, Alsaqour R, Abdelhaq S
    PLoS One, 2015;10(5):e0120715.
    PMID: 25946001 DOI: 10.1371/journal.pone.0120715
    A mobile ad hoc network (MANET) is a set of mobile, decentralized, and self-organizing nodes that are used in special cases, such as in the military. MANET properties render the environment of this network vulnerable to different types of attacks, including black hole, wormhole and flooding-based attacks. Flooding-based attacks are one of the most dangerous attacks that aim to consume all network resources and thus paralyze the functionality of the whole network. Therefore, the objective of this paper is to investigate the capability of a danger theory-based artificial immune algorithm called the mobile dendritic cell algorithm (MDCA) to detect flooding-based attacks in MANETs. The MDCA applies the dendritic cell algorithm (DCA) to secure the MANET with additional improvements. The MDCA is tested and validated using Qualnet v7.1 simulation tool. This work also introduces a new simulation module for a flooding attack called the resource consumption attack (RCA) using Qualnet v7.1. The results highlight the high efficiency of the MDCA in detecting RCAs in MANETs.
    Matched MeSH terms: Neural Networks (Computer)*
  10. Ehteram M, Ahmed AN, Latif SD, Huang YF, Alizamir M, Kisi O, et al.
    Environ Sci Pollut Res Int, 2021 Jan;28(2):1596-1611.
    PMID: 32851519 DOI: 10.1007/s11356-020-10421-y
    There is a need to develop an accurate and reliable model for predicting suspended sediment load (SSL) because of its complexity and difficulty in practice. This is due to the fact that sediment transportation is extremely nonlinear and is directed by numerous parameters such as rainfall, sediment supply, and strength of flow. Thus, this study examined two scenarios to investigate the effectiveness of the artificial neural network (ANN) models and determine the sensitivity of the predictive accuracy of the model to specific input parameters. The first scenario proposed three advanced optimisers-whale algorithm (WA), particle swarm optimization (PSO), and bat algorithm (BA)-for the optimisation of the performance of artificial neural network (ANN) in accurately predicting the suspended sediment load rate at the Goorganrood basin, Iran. In total, 5 different input combinations were examined in various lag days of up to 5 days to make a 1-day-ahead SSL prediction. Scenario 2 introduced a multi-objective (MO) optimisation algorithm that utilises the same inputs from scenario 1 as a way of determining the best combination of inputs. Results from scenario 1 revealed that high accuracy levels were achieved upon utilisation of a hybrid ANN-WA model over the ANN-BA with an RMSE value ranging from 1 to 6%. Furthermore, the ANN-WA model performed better than the ANN-PSO with an accuracy improvement value of 5-20%. Scenario 2 achieved the highest R2 when ANN-MOWA was introduced which shows that hybridisation of the multi-objective algorithm with WA and ANN model significantly improves the accuracy of ANN in predicting the daily suspended sediment load.
    Matched MeSH terms: Neural Networks (Computer)*
  11. Zulfiqar M, Chowdhury S, Omar AA, Siyal AA, Sufian S
    Environ Sci Pollut Res Int, 2020 Sep;27(27):34018-34036.
    PMID: 32557068 DOI: 10.1007/s11356-020-09674-4
    The primary responsibility for continuously discharging toxic organic pollutants into water bodies and open environments is the increase in industrial and agricultural activities. Developing economical and suitable methods to continuously remove organic pollutants from wastewater is highly essential. The aim of the present research was to apply response surface methodology (RSM) and artificial neural networks (ANNs) for optimization and modeling of photocatalytic degradation of acid orange 7 (AO7) by commercial TiO2-P25 nanoparticles (TNPs). Dose of TNPs, pH, and AO7 concentration were selected as investigated parameters. RSM results reveal the reflective rate of AO7 removal of ~ 94.974% was obtained at pH 7.599, TNP dose of 0.748 g/L, and AO7 concentration of 28.483 mg/L. The resulting quadratic model is satisfactory with the highest coefficient of determination (R2) between the predicted and experimental data (R2 = 0.98 and adjusted R2 = 0.954). On the other hand, ANNs were successfully employed for modeling of AO7 degradation process. The proposed ANN model was absolutely fitted with experimental results producing the highest R2. Furthermore, root mean square error (RMSE), mean average deviation (MAD), absolute average relative error (AARE), and mean square error (MSE) were examined more to compare the predictive capabilities of ANN and RSM models. The experimental data was well fitted into pseudo-first-order and pseudo-second-order kinetics with more accuracy. Thermodynamic parameters, namely enthalpy, entropy, Gibbs' free energy, and activation energy, were also evaluated to suggest the nature of the degradation process. The increase of temperature was analyzed to be more suitable for the fast removal of AO7 over TNPs. Graphical abstract.
    Matched MeSH terms: Neural Networks (Computer)*
  12. Siavash NK, Ghobadian B, Najafi G, Rohani A, Tavakoli T, Mahmoodi E, et al.
    Environ Res, 2021 05;196:110434.
    PMID: 33166537 DOI: 10.1016/j.envres.2020.110434
    Wind power is one of the most popular sources of renewable energies with an ideal extractable value that is limited to 0.593 known as the Betz-Joukowsky limit. As the generated power of wind machines is proportional to cubic wind speed, therefore it is logical that a small increment in wind speed will result in significant growth in generated power. Shrouding a wind turbine is an ordinary way to exceed the Betz limit, which accelerates the wind flow through the rotor plane. Several layouts of shrouds are developed by researchers. Recently an innovative controllable duct is developed by the authors of this work that can vary the shrouding angle, so its performance is different in each opening angle. As a wind tunnel investigation is heavily time-consuming and has a high cost, therefore just four different opening angles have been assessed. In this work, the performance of the turbine was predicted using multiple linear regression and an artificial neural network in a wide range of duct opening angles. For the turbine power generation and its rotor angular speed in different wind velocities and duct opening angles, regression and an ANN are suggested. The developed neural network model is found to possess better performance than the regression model for both turbine power curve and rotor speed estimation. This work revealed that in higher ranges of wind velocity, the turbine performance intensively will be a function of shrouding angle. This model can be used as a lookup table in controlling the turbines equipped with the proposed mechanism.
    Matched MeSH terms: Neural Networks (Computer)*
  13. Abdollahi A, Pradhan B
    Sensors (Basel), 2021 Jul 11;21(14).
    PMID: 34300478 DOI: 10.3390/s21144738
    Urban vegetation mapping is critical in many applications, i.e., preserving biodiversity, maintaining ecological balance, and minimizing the urban heat island effect. It is still challenging to extract accurate vegetation covers from aerial imagery using traditional classification approaches, because urban vegetation categories have complex spatial structures and similar spectral properties. Deep neural networks (DNNs) have shown a significant improvement in remote sensing image classification outcomes during the last few years. These methods are promising in this domain, yet unreliable for various reasons, such as the use of irrelevant descriptor features in the building of the models and lack of quality in the labeled image. Explainable AI (XAI) can help us gain insight into these limits and, as a result, adjust the training dataset and model as needed. Thus, in this work, we explain how an explanation model called Shapley additive explanations (SHAP) can be utilized for interpreting the output of the DNN model that is designed for classifying vegetation covers. We want to not only produce high-quality vegetation maps, but also rank the input parameters and select appropriate features for classification. Therefore, we test our method on vegetation mapping from aerial imagery based on spectral and textural features. Texture features can help overcome the limitations of poor spectral resolution in aerial imagery for vegetation mapping. The model was capable of obtaining an overall accuracy (OA) of 94.44% for vegetation cover mapping. The conclusions derived from SHAP plots demonstrate the high contribution of features, such as Hue, Brightness, GLCM_Dissimilarity, GLCM_Homogeneity, and GLCM_Mean to the output of the proposed model for vegetation mapping. Therefore, the study indicates that existing vegetation mapping strategies based only on spectral characteristics are insufficient to appropriately classify vegetation covers.
    Matched MeSH terms: Neural Networks (Computer)*
  14. Koay HV, Chuah JH, Chow CO, Chang YL, Rudrusamy B
    Sensors (Basel), 2021 Jul 15;21(14).
    PMID: 34300577 DOI: 10.3390/s21144837
    Distracted driving is the prime factor of motor vehicle accidents. Current studies on distraction detection focus on improving distraction detection performance through various techniques, including convolutional neural networks (CNNs) and recurrent neural networks (RNNs). However, the research on detection of distracted drivers through pose estimation is scarce. This work introduces an ensemble of ResNets, which is named Optimally-weighted Image-Pose Approach (OWIPA), to classify the distraction through original and pose estimation images. The pose estimation images are generated from HRNet and ResNet. We use ResNet101 and ResNet50 to classify the original images and the pose estimation images, respectively. An optimum weight is determined through grid search method, and the predictions from both models are weighted through this parameter. The experimental results show that our proposed approach achieves 94.28% accuracy on AUC Distracted Driver Dataset.
    Matched MeSH terms: Neural Networks (Computer)*
  15. Hai A, Bharath G, Daud M, Rambabu K, Ali I, Hasan SW, et al.
    Chemosphere, 2021 Nov;283:131162.
    PMID: 34157626 DOI: 10.1016/j.chemosphere.2021.131162
    Pyrolysis of agricultural biomass is a promising technique for producing renewable energy and effectively managing solid waste. In this study, groundnut shell (GNS) was processed at 500 °C in an inert gas atmosphere with a gas flow rate and a heating rate of 10 mL/min and 10 °C/min, respectively, in a custom-designed fluidized bed pyrolytic-reactor. Under optimal operating conditions, the GNS-derived pyrolytic-oil yield was 62.8 wt.%, with the corresponding biochar (19.5 wt.%) and biogas yields (17.7 wt.%). The GC-MS analysis of the GNS-based bio-oil confirmed the presence of (trifluoromethyl)pyridin-2-amine (18.814%), 2-Fluoroformyl-3,3,4,4-tetrafluoro-1,2-oxazetidine (16.23%), 5,7-dimethyl-1H-Indazole (11.613%), N-methyl-N-nitropropan-2-amine (6.5%) and butyl piperidino sulfone (5.668%) as major components, which are used as building blocks in the biofuel, pharmaceutical, and food industries. Furthermore, a 2 × 5 × 1 artificial neural network (ANN) architecture was developed to predict the decomposition behavior of GNS at heating rates of 5, 10, and 20 °C/min, while the thermodynamic and kinetic parameters were estimated using a non-isothermal model-free method. The Popescu method predicted activation energy (Ea) of GNS biomass ranging from 111 kJ/mol to 260 kJ/mol, with changes in enthalpy (ΔH), Gibbs-free energy (ΔG), and entropy (ΔS) ranging from 106 to 254 kJ/mol, 162-241 kJ/mol, and -0.0937 to 0.0598 kJ/mol/K, respectively. The extraction of high-quality precursors from GNS pyrolysis was demonstrated in this study, as well as the usefulness of the ANN technique for thermogravimetric analysis of biomass.
    Matched MeSH terms: Neural Networks (Computer)*
  16. Nisar K, Sabir Z, Zahoor Raja MA, Ibrahim AAA, Mahmoud SR, Balubaid M, et al.
    Sensors (Basel), 2021 Sep 30;21(19).
    PMID: 34640887 DOI: 10.3390/s21196567
    In this study, the numerical computation heuristic of the environmental and economic system using the artificial neural networks (ANNs) structure together with the capabilities of the heuristic global search genetic algorithm (GA) and the quick local search interior-point algorithm (IPA), i.e., ANN-GA-IPA. The environmental and economic system is dependent of three categories, execution cost of control standards and new technical diagnostics elimination costs of emergencies values and the competence of the system of industrial elements. These three elements form a nonlinear differential environmental and economic system. The optimization of an error-based objective function is performed using the differential environmental and economic system and its initial conditions. The optimization of an error-based objective function is performed using the differential environmental and economic system and its initial conditions.
    Matched MeSH terms: Neural Networks (Computer)*
  17. Mohamed NA, Zulkifley MA, Ibrahim AA, Aouache M
    Sensors (Basel), 2021 Sep 28;21(19).
    PMID: 34640803 DOI: 10.3390/s21196485
    In recent years, there has been an immense amount of research into fall event detection. Generally, a fall event is defined as a situation in which a person unintentionally drops down onto a lower surface. It is crucial to detect the occurrence of fall events as early as possible so that any severe fall consequences can be minimized. Nonetheless, a fall event is a sporadic incidence that occurs seldomly that is falsely detected due to a wide range of fall conditions and situations. Therefore, an automated fall frame detection system, which is referred to as the SmartConvFall is proposed to detect the exact fall frame in a video sequence. It is crucial to know the exact fall frame as it dictates the response time of the system to administer an early treatment to reduce the fall's negative consequences and related injuries. Henceforth, searching for the optimal training configurations is imperative to ensure the main goal of the SmartConvFall is achieved. The proposed SmartConvFall consists of two parts, which are object tracking and instantaneous fall frame detection modules that rely on deep learning representations. The first stage will track the object of interest using a fully convolutional neural network (CNN) tracker. Various training configurations such as optimizer, learning rate, mini-batch size, number of training samples, and region of interest are individually evaluated to determine the best configuration to produce the best tracker model. Meanwhile, the second module goal is to determine the exact instantaneous fall frame by modeling the continuous object trajectories using the Long Short-Term Memory (LSTM) network. Similarly, the LSTM model will undergo various training configurations that cover different types of features selection and the number of stacked layers. The exact instantaneous fall frame is determined using an assumption that a large movement difference with respect to the ground level along the vertical axis can be observed if a fall incident happened. The proposed SmartConvFall is a novel technique as most of the existing methods still relying on detection rather than the tracking module. The SmartConvFall outperforms the state-of-the-art trackers, namely TCNN and MDNET-N trackers, with the highest expected average overlap, robustness, and reliability metrics of 0.1619, 0.6323, and 0.7958, respectively. The SmartConvFall also managed to produce the lowest number of tracking failures with only 43 occasions. Moreover, a three-stack LSTM delivers the lowest mean error with approximately one second delay time in locating the exact instantaneous fall frame. Therefore, the proposed SmartConvFall has demonstrated its potential and suitability to be implemented for a real-time application that could help to avoid any crucial fall consequences such as death and internal bleeding if the early treatment can be administered.
    Matched MeSH terms: Neural Networks (Computer)*
  18. Waleeda Swaidan, Amran Hussin
    Sains Malaysiana, 2016;45:305-313.
    A new numerical method was proposed in this paper to address the nonlinear quadratic optimal control problems, with state and control inequality constraints. This method used the quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a sequence of quadratic programming problems. The inequality constraints for trajectory variables were transformed into quadratic programming constraints using the Haar wavelet collocation method. The proposed method was applied to optimize the control of the multi-item inventory model with linear demand rates. By enhancing the resolution of the Haar wavelet, we can improve the accuracy of the states, controls and cost. Simulation results were also compared with other researchers' work.
  19. Ullah, Hadaate, Kiber, Adnan, Huq, Asadul, Mohammad Arif Sobhan Bhuiyan
    MyJurnal
    Classification is one of the most hourly encountered problems in real world. Neural networks have
    emerged as one of the tools that can handle the classification problem. Feed-Forward Neural Networks
    (FFNN's) have been widely applied in many different fields as a classification tool. Designing an efficient
    FFNN structure with the optimum number of hidden layers and minimum number of layer's neurons for
    a given specific application or dataset, is an open research problem and more challenging depend on
    the input data. The random selections of hidden layers and neurons may cause the problem of either
    under fitting or over fitting. Over fitting arises because the network matches the data so closely as to
    lose its generalization ability over the test data. In this research, the classification performance using
    the Mean Square Error (MSE) of Feed-Forward Neural Network (FFNN) with back-propagation algorithm
    with respect to the different number of hidden layers and hidden neurons is computed and analyzed to
    find out the optimum number of hidden layers and minimum number of layer's neurons to help the
    existing classification concepts by MATLAB version 13a. By this process, firstly the random data has
    been generated using an suitable matlab function to prepare the training data as the input and target
    vectors as the testing data for the classification purposes of FFNN. The generated input data is passed
    on to the output layer through the hidden layers which process these data. From this analysis, it is find
    out from the mean square error comparison graphs and regression plots that for getting the best
    performance form this network, it is better to use the high number of hidden layers and more neurons in
    the hidden layers in the network during designing its classifier but so more neurons in the hidden layers
    and the high number of hidden layers in the network makes it complex and takes more time to execute.
    So as the result it is suggested that three hidden layers and 26 hidden neurons in each hidden layers
    are better for designing the classifier of this network for this type of input data features.
  20. Mohd. Asrul Hery Bin Ibrahim, Mustafa Mamat, Leong Wah June
    Sains Malaysiana, 2014;43:1591-1597.
    In this paper we present a new line search method known as the HBFGS method, which uses the search direction of the conjugate gradient method with the quasi-Newton updates. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) update is used as approximation of the Hessian for the methods. The new algorithm is compared with the BFGS method in terms of iteration counts and CPU-time. Our numerical analysis provides strong evidence that the proposed HBFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent.
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