This study proposes a novel time-synchronization protocol inspired by stochastic gradient algorithms.The clock model of each network node in this synchronizer is configured as a generic adaptive filter where different...This study proposes a novel time-synchronization protocol inspired by stochastic gradient algorithms.The clock model of each network node in this synchronizer is configured as a generic adaptive filter where different stochastic gradient algorithms can be adopted for adaptive clock frequency adjustments.The study analyzes the pairwise synchronization behavior of the protocol and proves the generalized convergence of the synchronization error and clock frequency.A novel closed-form expression is also derived for a generalized asymptotic error variance steady state.Steady and convergence analyses are then presented for the synchronization,with frequency adaptations done using least mean square(LMS),the Newton search,the gradient descent(GraDes),the normalized LMS(N-LMS),and the Sign-Data LMS algorithms.Results obtained from real-time experiments showed a better performance of our protocols as compared to the Average Proportional-Integral Synchronization Protocol(AvgPISync)regarding the impact of quantization error on synchronization accuracy,precision,and convergence time.This generalized approach to time synchronization allows flexibility in selecting a suitable protocol for different wireless sensor network applications.展开更多
We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (...We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.展开更多
A recommender system(RS)relying on latent factor analysis usually adopts stochastic gradient descent(SGD)as its learning algorithm.However,owing to its serial mechanism,an SGD algorithm suffers from low efficiency and...A recommender system(RS)relying on latent factor analysis usually adopts stochastic gradient descent(SGD)as its learning algorithm.However,owing to its serial mechanism,an SGD algorithm suffers from low efficiency and scalability when handling large-scale industrial problems.Aiming at addressing this issue,this study proposes a momentum-incorporated parallel stochastic gradient descent(MPSGD)algorithm,whose main idea is two-fold:a)implementing parallelization via a novel datasplitting strategy,and b)accelerating convergence rate by integrating momentum effects into its training process.With it,an MPSGD-based latent factor(MLF)model is achieved,which is capable of performing efficient and high-quality recommendations.Experimental results on four high-dimensional and sparse matrices generated by industrial RS indicate that owing to an MPSGD algorithm,an MLF model outperforms the existing state-of-the-art ones in both computational efficiency and scalability.展开更多
Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, a...Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, assuming that the training examples are input in a stochastic way. The monotonicity of the error function in the iteration and the boundedness of the weight are both guaranteed. We also present a numerical experiment to support our results.展开更多
Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to rea...Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to realize the identification and separation of the Hammerstein model.As a result,the identification of the dynamic linear part can be separated from the static nonlinear elements without any redundant adjustable parameters.The auxiliary model based multi-innovation stochastic gradient algorithm was applied to identifying the serial link parameters of the Hammerstein model.The auxiliary model based multi-innovation stochastic gradient algorithm can avoid the influence of noise and improve the identification accuracy by changing the innovation length.The simulation results show the efficiency of the proposed method.展开更多
The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochast...The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.展开更多
The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of...The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.展开更多
Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term.Proximal stochastic gradient methods are popular for solving such composite optimization proble...Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term.Proximal stochastic gradient methods are popular for solving such composite optimization problems.We propose a minibatch proximal stochastic recursive gradient algorithm SRG-DBB,which incorporates the diagonal Barzilai–Borwein(DBB)stepsize strategy to capture the local geometry of the problem.The linear convergence and complexity of SRG-DBB are analyzed for strongly convex functions.We further establish the linear convergence of SRGDBB under the non-strong convexity condition.Moreover,it is proved that SRG-DBB converges sublinearly in the convex case.Numerical experiments on standard data sets indicate that the performance of SRG-DBB is better than or comparable to the proximal stochastic recursive gradient algorithm with best-tuned scalar stepsizes or BB stepsizes.Furthermore,SRG-DBB is superior to some advanced mini-batch proximal stochastic gradient methods.展开更多
Direct sequence spread spectrum transmission can be realized at low SNR, and has low probabilityof detection. It is aly problem how to obtain the original users＇ signal in a non-cooperative context. In practicality, ...Direct sequence spread spectrum transmission can be realized at low SNR, and has low probabilityof detection. It is aly problem how to obtain the original users＇ signal in a non-cooperative context. In practicality, the DS/CDMA sources received are linear convolute mixing. A more complex multichannel blind deconvolution MBD algorithm is required to achieve better source separation. An improved MBD algorithm for separating linear convolved mixtures of signals in CDMA system is proposed. This algorithm is based on minimizing the average squared cross-output-channel-correlation. The mixture coefficients are totally unknown, while some knowledge about temporal model exists. Results show that the proposed algorithm can bring about the exactness and low computational complexity.展开更多
Distributed optimization has been well developed in recent years due to its wide applications in machine learning and signal processing.In this paper,we focus on investigating distributed optimization to minimize a gl...Distributed optimization has been well developed in recent years due to its wide applications in machine learning and signal processing.In this paper,we focus on investigating distributed optimization to minimize a global objective.The objective is a sum of smooth and strongly convex local cost functions which are distributed over an undirected network of n nodes.In contrast to existing works,we apply a distributed heavy-ball term to improve the convergence performance of the proposed algorithm.To accelerate the convergence of existing distributed stochastic first-order gradient methods,a momentum term is combined with a gradient-tracking technique.It is shown that the proposed algorithm has better acceleration ability than GT-SAGA without increasing the complexity.Extensive experiments on real-world datasets verify the effectiveness and correctness of the proposed algorithm.展开更多
Datamining plays a crucial role in extractingmeaningful knowledge fromlarge-scale data repositories,such as data warehouses and databases.Association rule mining,a fundamental process in data mining,involves discoveri...Datamining plays a crucial role in extractingmeaningful knowledge fromlarge-scale data repositories,such as data warehouses and databases.Association rule mining,a fundamental process in data mining,involves discovering correlations,patterns,and causal structures within datasets.In the healthcare domain,association rules offer valuable opportunities for building knowledge bases,enabling intelligent diagnoses,and extracting invaluable information rapidly.This paper presents a novel approach called the Machine Learning based Association Rule Mining and Classification for Healthcare Data Management System(MLARMC-HDMS).The MLARMC-HDMS technique integrates classification and association rule mining(ARM)processes.Initially,the chimp optimization algorithm-based feature selection(COAFS)technique is employed within MLARMC-HDMS to select relevant attributes.Inspired by the foraging behavior of chimpanzees,the COA algorithm mimics their search strategy for food.Subsequently,the classification process utilizes stochastic gradient descent with a multilayer perceptron(SGD-MLP)model,while the Apriori algorithm determines attribute relationships.We propose a COA-based feature selection approach for medical data classification using machine learning techniques.This approach involves selecting pertinent features from medical datasets through COA and training machine learning models using the reduced feature set.We evaluate the performance of our approach on various medical datasets employing diverse machine learning classifiers.Experimental results demonstrate that our proposed approach surpasses alternative feature selection methods,achieving higher accuracy and precision rates in medical data classification tasks.The study showcases the effectiveness and efficiency of the COA-based feature selection approach in identifying relevant features,thereby enhancing the diagnosis and treatment of various diseases.To provide further validation,we conduct detailed experiments on a benchmark medical dataset,revealing the superiority of the MLARMCHDMS model over other methods,with a maximum accuracy of 99.75%.Therefore,this research contributes to the advancement of feature selection techniques in medical data classification and highlights the potential for improving healthcare outcomes through accurate and efficient data analysis.The presented MLARMC-HDMS framework and COA-based feature selection approach offer valuable insights for researchers and practitioners working in the field of healthcare data mining and machine learning.展开更多
Dear Editor,Through distributed machine learning,multi-UAV systems can achieve global optimization goals without a centralized server,such as optimal target tracking,by leveraging local calculation and communication w...Dear Editor,Through distributed machine learning,multi-UAV systems can achieve global optimization goals without a centralized server,such as optimal target tracking,by leveraging local calculation and communication with neighbors.In this work,we implement the stochastic gradient descent algorithm(SGD)distributedly to optimize tracking errors based on local state and aggregation of the neighbors'estimation.However,Byzantine agents can mislead neighbors,causing deviations from optimal tracking.We prove that the swarm achieves resilient convergence if aggregated results lie within the normal neighbors'convex hull,which can be guaranteed by the introduced centerpoint-based aggregation rule.In the given simulated scenarios,distributed learning using average,geometric median(GM),and coordinate-wise median(CM)based aggregation rules fail to track the target.Compared to solely using the centerpoint aggregation method,our approach,which combines a pre-filter with the centroid aggregation rule,significantly enhances resilience against Byzantine attacks,achieving faster convergence and smaller tracking errors.展开更多
In this paper,a multi-product newsvendor problem is formulated as a random nonlinear integrated optimization model by taking into consideration the selling price,the producing and outsourcing quantities,and the nonlin...In this paper,a multi-product newsvendor problem is formulated as a random nonlinear integrated optimization model by taking into consideration the selling price,the producing and outsourcing quantities,and the nonlinear budget constraint.Different from the existing models,the demands of products depend on the prices,as well as being timevarying due to random market fluctuation.In addition,outsourcing strategy is adopted to deal with possible shortage caused by the limited capacity.Consequently,the constructed model is involved with joint optimization of the producing and outsourcing quantities,and the selling prices of all the products.For this model with continuous random demands,we first transform it into a nonlinear programming problem by expectation method.Then,an efficient algorithm,called the feasible-direction-based spectral conjugate gradient algorithm,is developed to find a robust solution of the model.By case study and sensitivity analysis,some interesting conclusions are drawn as follows:(a)Budget is a critical constraint for optimizing the decision-making of the retailer,and there exist different threshold values of the budget for the substitute and complementarity scenarios.(b)The price sensitivity matrix seriously affects the maximal expected profit mainly through affecting the optimal outsourcing quantity.展开更多
基金funded by Universiti Putra Malaysia under a Geran Putra Inisiatif(GPI)research grant with reference to GP-GPI/2023/9762100.
文摘This study proposes a novel time-synchronization protocol inspired by stochastic gradient algorithms.The clock model of each network node in this synchronizer is configured as a generic adaptive filter where different stochastic gradient algorithms can be adopted for adaptive clock frequency adjustments.The study analyzes the pairwise synchronization behavior of the protocol and proves the generalized convergence of the synchronization error and clock frequency.A novel closed-form expression is also derived for a generalized asymptotic error variance steady state.Steady and convergence analyses are then presented for the synchronization,with frequency adaptations done using least mean square(LMS),the Newton search,the gradient descent(GraDes),the normalized LMS(N-LMS),and the Sign-Data LMS algorithms.Results obtained from real-time experiments showed a better performance of our protocols as compared to the Average Proportional-Integral Synchronization Protocol(AvgPISync)regarding the impact of quantization error on synchronization accuracy,precision,and convergence time.This generalized approach to time synchronization allows flexibility in selecting a suitable protocol for different wireless sensor network applications.
文摘We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.
基金supported in part by the National Natural Science Foundation of China(61772493)the Deanship of Scientific Research(DSR)at King Abdulaziz University(RG-48-135-40)+1 种基金Guangdong Province Universities and College Pearl River Scholar Funded Scheme(2019)the Natural Science Foundation of Chongqing(cstc2019jcyjjqX0013)。
文摘A recommender system(RS)relying on latent factor analysis usually adopts stochastic gradient descent(SGD)as its learning algorithm.However,owing to its serial mechanism,an SGD algorithm suffers from low efficiency and scalability when handling large-scale industrial problems.Aiming at addressing this issue,this study proposes a momentum-incorporated parallel stochastic gradient descent(MPSGD)algorithm,whose main idea is two-fold:a)implementing parallelization via a novel datasplitting strategy,and b)accelerating convergence rate by integrating momentum effects into its training process.With it,an MPSGD-based latent factor(MLF)model is achieved,which is capable of performing efficient and high-quality recommendations.Experimental results on four high-dimensional and sparse matrices generated by industrial RS indicate that owing to an MPSGD algorithm,an MLF model outperforms the existing state-of-the-art ones in both computational efficiency and scalability.
基金Partly supported by the National Natural Science Foundation of China,and the Basic Research Program of the Committee of ScienceTechnology and Industry of National Defense of China.
文摘Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, assuming that the training examples are input in a stochastic way. The monotonicity of the error function in the iteration and the boundedness of the weight are both guaranteed. We also present a numerical experiment to support our results.
基金National Natural Science Foundation of China(No.61374044)Shanghai Science Technology Commission,China(Nos.15510722100,16111106300)
文摘Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to realize the identification and separation of the Hammerstein model.As a result,the identification of the dynamic linear part can be separated from the static nonlinear elements without any redundant adjustable parameters.The auxiliary model based multi-innovation stochastic gradient algorithm was applied to identifying the serial link parameters of the Hammerstein model.The auxiliary model based multi-innovation stochastic gradient algorithm can avoid the influence of noise and improve the identification accuracy by changing the innovation length.The simulation results show the efficiency of the proposed method.
基金National Natural Science Foundation of China(Nos.4156108241161061)。
文摘The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.
基金supported by the Knut and Alice Wallenberg Foundationthe Swedish Foundation for Strategic Research+1 种基金the Swedish Research Councilthe National Natural Science Foundation of China(62133003,61991403,61991404,61991400)。
文摘The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.
基金the National Natural Science Foundation of China(Nos.11671116,11701137,12071108,11991020,11991021 and 12021001)the Major Research Plan of the NSFC(No.91630202)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA27000000)the Natural Science Foundation of Hebei Province(No.A2021202010)。
文摘Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term.Proximal stochastic gradient methods are popular for solving such composite optimization problems.We propose a minibatch proximal stochastic recursive gradient algorithm SRG-DBB,which incorporates the diagonal Barzilai–Borwein(DBB)stepsize strategy to capture the local geometry of the problem.The linear convergence and complexity of SRG-DBB are analyzed for strongly convex functions.We further establish the linear convergence of SRGDBB under the non-strong convexity condition.Moreover,it is proved that SRG-DBB converges sublinearly in the convex case.Numerical experiments on standard data sets indicate that the performance of SRG-DBB is better than or comparable to the proximal stochastic recursive gradient algorithm with best-tuned scalar stepsizes or BB stepsizes.Furthermore,SRG-DBB is superior to some advanced mini-batch proximal stochastic gradient methods.
基金the National Natural Science Foundation of China (60472052,10577007)the Specialized Research Fund for National Key Lab of Communication (51434020105ZS04).
文摘Direct sequence spread spectrum transmission can be realized at low SNR, and has low probabilityof detection. It is aly problem how to obtain the original users＇ signal in a non-cooperative context. In practicality, the DS/CDMA sources received are linear convolute mixing. A more complex multichannel blind deconvolution MBD algorithm is required to achieve better source separation. An improved MBD algorithm for separating linear convolved mixtures of signals in CDMA system is proposed. This algorithm is based on minimizing the average squared cross-output-channel-correlation. The mixture coefficients are totally unknown, while some knowledge about temporal model exists. Results show that the proposed algorithm can bring about the exactness and low computational complexity.
基金Project supported by the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province,China(No.DRN2001)the National Natural Science Foundation of China(Nos.61773321 and 61762020)+2 种基金the Science and Technology Top-Notch Talents Support Project of Colleges and Universities in Guizhou Province,China(No.QJHKY2016065)the Science and Technology Foundation of Guizhou Province,China(No.QKHJC20181083)the Science and Technology Talents Fund for Excellent Young of Guizhou Province,China(No.QKHPTRC20195669)。
文摘Distributed optimization has been well developed in recent years due to its wide applications in machine learning and signal processing.In this paper,we focus on investigating distributed optimization to minimize a global objective.The objective is a sum of smooth and strongly convex local cost functions which are distributed over an undirected network of n nodes.In contrast to existing works,we apply a distributed heavy-ball term to improve the convergence performance of the proposed algorithm.To accelerate the convergence of existing distributed stochastic first-order gradient methods,a momentum term is combined with a gradient-tracking technique.It is shown that the proposed algorithm has better acceleration ability than GT-SAGA without increasing the complexity.Extensive experiments on real-world datasets verify the effectiveness and correctness of the proposed algorithm.
基金Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia for funding this research work through the Project Number RI-44-0444.
文摘Datamining plays a crucial role in extractingmeaningful knowledge fromlarge-scale data repositories,such as data warehouses and databases.Association rule mining,a fundamental process in data mining,involves discovering correlations,patterns,and causal structures within datasets.In the healthcare domain,association rules offer valuable opportunities for building knowledge bases,enabling intelligent diagnoses,and extracting invaluable information rapidly.This paper presents a novel approach called the Machine Learning based Association Rule Mining and Classification for Healthcare Data Management System(MLARMC-HDMS).The MLARMC-HDMS technique integrates classification and association rule mining(ARM)processes.Initially,the chimp optimization algorithm-based feature selection(COAFS)technique is employed within MLARMC-HDMS to select relevant attributes.Inspired by the foraging behavior of chimpanzees,the COA algorithm mimics their search strategy for food.Subsequently,the classification process utilizes stochastic gradient descent with a multilayer perceptron(SGD-MLP)model,while the Apriori algorithm determines attribute relationships.We propose a COA-based feature selection approach for medical data classification using machine learning techniques.This approach involves selecting pertinent features from medical datasets through COA and training machine learning models using the reduced feature set.We evaluate the performance of our approach on various medical datasets employing diverse machine learning classifiers.Experimental results demonstrate that our proposed approach surpasses alternative feature selection methods,achieving higher accuracy and precision rates in medical data classification tasks.The study showcases the effectiveness and efficiency of the COA-based feature selection approach in identifying relevant features,thereby enhancing the diagnosis and treatment of various diseases.To provide further validation,we conduct detailed experiments on a benchmark medical dataset,revealing the superiority of the MLARMCHDMS model over other methods,with a maximum accuracy of 99.75%.Therefore,this research contributes to the advancement of feature selection techniques in medical data classification and highlights the potential for improving healthcare outcomes through accurate and efficient data analysis.The presented MLARMC-HDMS framework and COA-based feature selection approach offer valuable insights for researchers and practitioners working in the field of healthcare data mining and machine learning.
基金supported By Guangdong Major Project of Basic and Applied Basic Research(2023B0303000009)Guangdong Basic and Applied Basic Research Foundation(2024A1515030153,2025A1515011587)+1 种基金Project of Department of Education of Guangdong Province(2023ZDZX4046)Shen-zhen Natural Science Fund(Stable Support Plan Program 20231122121608001),Ningbo Municipal Science and Technology Bureau(ZX2024000604).
文摘Dear Editor,Through distributed machine learning,multi-UAV systems can achieve global optimization goals without a centralized server,such as optimal target tracking,by leveraging local calculation and communication with neighbors.In this work,we implement the stochastic gradient descent algorithm(SGD)distributedly to optimize tracking errors based on local state and aggregation of the neighbors'estimation.However,Byzantine agents can mislead neighbors,causing deviations from optimal tracking.We prove that the swarm achieves resilient convergence if aggregated results lie within the normal neighbors'convex hull,which can be guaranteed by the introduced centerpoint-based aggregation rule.In the given simulated scenarios,distributed learning using average,geometric median(GM),and coordinate-wise median(CM)based aggregation rules fail to track the target.Compared to solely using the centerpoint aggregation method,our approach,which combines a pre-filter with the centroid aggregation rule,significantly enhances resilience against Byzantine attacks,achieving faster convergence and smaller tracking errors.
基金supported by National Natural Science Foundation of China(Grant No.71671190)。
文摘In this paper,a multi-product newsvendor problem is formulated as a random nonlinear integrated optimization model by taking into consideration the selling price,the producing and outsourcing quantities,and the nonlinear budget constraint.Different from the existing models,the demands of products depend on the prices,as well as being timevarying due to random market fluctuation.In addition,outsourcing strategy is adopted to deal with possible shortage caused by the limited capacity.Consequently,the constructed model is involved with joint optimization of the producing and outsourcing quantities,and the selling prices of all the products.For this model with continuous random demands,we first transform it into a nonlinear programming problem by expectation method.Then,an efficient algorithm,called the feasible-direction-based spectral conjugate gradient algorithm,is developed to find a robust solution of the model.By case study and sensitivity analysis,some interesting conclusions are drawn as follows:(a)Budget is a critical constraint for optimizing the decision-making of the retailer,and there exist different threshold values of the budget for the substitute and complementarity scenarios.(b)The price sensitivity matrix seriously affects the maximal expected profit mainly through affecting the optimal outsourcing quantity.
