A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gr...A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.展开更多
空气质量是生态环境保护的一个重要指标,准确的空气质量预测能够帮助政府和相关机构采取有效的应对措施,减少空气污染带来的负面影响,因此空气质量等级预测对于社会发展和生态文明建设十分重要。本文基于2023年浙江省的空气质量样本数据...空气质量是生态环境保护的一个重要指标,准确的空气质量预测能够帮助政府和相关机构采取有效的应对措施,减少空气污染带来的负面影响,因此空气质量等级预测对于社会发展和生态文明建设十分重要。本文基于2023年浙江省的空气质量样本数据,通过比较常见的3种机器学习算法,选择以BP神经网络为基模型,探究BFGS-BP神经网络模型的预测能力。研究表明,BFGS-BP神经网络模型能较好地对城市的空气质量指数进行预测,准确率较高。说明该模型存在着相应的参考价值和现实意义,为我国空气污染防治工作提供了有力支持。在此基础上,进一步推广和应用该模型,有助于提高我国空气质量管理的科学性和有效性。Air quality is a crucial indicator for ecological environmental protection. Accurate air quality forecasting can assist governments and relevant institutions in taking effective measures to mitigate the negative impacts of air pollution. Therefore, the prediction of air quality levels is of great importance for social development and the construction of an ecological civilization. Based on the air quality sample data from Zhejiang Province in 2023, this paper compares three common machine learning algorithms and selects the BP neural network as the base model to explore the predictive capabilities of the BFGS-BP neural network model. The research indicates that the BFGS-BP neural network model can predict the city’s Air Quality Index (AQI) quite well, with a high accuracy rate. This demonstrates the model’s significant reference value and practical significance, providing strong support for China’s air pollution prevention and control efforts. Further promotion and application of this model will help enhance the scientificity and effectiveness of China’s air quality management.展开更多
基金supported by the Guangxi Science and Technology base and Talent Project(AD22080047)the National Natural Science Foundation of Guangxi Province(2023GXNFSBA 026063)+1 种基金the Innovation Funds of Chinese University(2021BCF03001)the special foundation for Guangxi Ba Gui Scholars.
文摘A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.
文摘空气质量是生态环境保护的一个重要指标,准确的空气质量预测能够帮助政府和相关机构采取有效的应对措施,减少空气污染带来的负面影响,因此空气质量等级预测对于社会发展和生态文明建设十分重要。本文基于2023年浙江省的空气质量样本数据,通过比较常见的3种机器学习算法,选择以BP神经网络为基模型,探究BFGS-BP神经网络模型的预测能力。研究表明,BFGS-BP神经网络模型能较好地对城市的空气质量指数进行预测,准确率较高。说明该模型存在着相应的参考价值和现实意义,为我国空气污染防治工作提供了有力支持。在此基础上,进一步推广和应用该模型,有助于提高我国空气质量管理的科学性和有效性。Air quality is a crucial indicator for ecological environmental protection. Accurate air quality forecasting can assist governments and relevant institutions in taking effective measures to mitigate the negative impacts of air pollution. Therefore, the prediction of air quality levels is of great importance for social development and the construction of an ecological civilization. Based on the air quality sample data from Zhejiang Province in 2023, this paper compares three common machine learning algorithms and selects the BP neural network as the base model to explore the predictive capabilities of the BFGS-BP neural network model. The research indicates that the BFGS-BP neural network model can predict the city’s Air Quality Index (AQI) quite well, with a high accuracy rate. This demonstrates the model’s significant reference value and practical significance, providing strong support for China’s air pollution prevention and control efforts. Further promotion and application of this model will help enhance the scientificity and effectiveness of China’s air quality management.
