本文研究一类低秩矩阵优化问题,其中惩罚项为目标矩阵奇异值的l_(p)(0<p<1)正则函数.基于半阈值函数在稀疏/低秩恢复问题中的良好性能,本文提出奇异值半阈值(singular value half thresholding,SVHT)算法来求解l_(p)正则矩阵优化...本文研究一类低秩矩阵优化问题,其中惩罚项为目标矩阵奇异值的l_(p)(0<p<1)正则函数.基于半阈值函数在稀疏/低秩恢复问题中的良好性能,本文提出奇异值半阈值(singular value half thresholding,SVHT)算法来求解l_(p)正则矩阵优化问题.SVHT算法的主要迭代利用了子问题的闭式解,但与现有算法不同,其本质上是对目标函数在当前点进行局部1/2近似,而不是局部线性或局部二次近似.通过构造目标函数的Lipschitz和非Lipschitz近似函数,本文证明了SVHT算法生成序列的任意聚点都是问题的一阶稳定点.在数值实验中,利用模拟数据和实际图像数据的低秩矩阵补全问题对SVHT算法进行测试.大量的数值结果表明,SVHT算法对低秩矩阵优化问题在速度、精度和鲁棒性等方面都表现优异.展开更多
在许多经济模型中,决策者需要通过比较集值优化问题的目标函数来衡量支出以达到自身收益的最大。在电子商务视角下,本文讨论了有限理性下基于改进集的集合优化问题E-u-最小解集的Levitin-Polyak良定性和广义Levitin-Polyak良定性,并通...在许多经济模型中,决策者需要通过比较集值优化问题的目标函数来衡量支出以达到自身收益的最大。在电子商务视角下,本文讨论了有限理性下基于改进集的集合优化问题E-u-最小解集的Levitin-Polyak良定性和广义Levitin-Polyak良定性,并通过有限理性模型证明了该良定性的充分条件。此外,借助非线性分析的方法给出了集合优化问题(广义) Levitin-Polyak良定性的特征刻画。这些结果为电子商务在实际生活中的应用打下了夯实的理论基础。In many economic models, decision-makers need to measure expenditures by comparing the objective functions of set-valued optimization problems in order to achieve maximum benefit. Under the perspective of E-commerce, this paper studies the Levitin-Polyak well-posedness and generalized Levitin-Polyak well-posedness of E-u-minimal solution of set optimization problems under bounded rationality via improvement set. Furthermore, the sufficient condition of well-posedness is given by using a bounded rationality model. Besides, we obtain the characterization of (generalized) Levitin-Polyak well-posedness for the problem by utilizing nonlinear analysis method. These results have laid a solid theoretical foundation for the application of E-commerce in practical life.展开更多
随着新时代的蓬勃发展,电商领域取得了历史性突破,但也伴随着许多不确定性问题显现。随机广义Nash均衡是非合作博弈的重要概念,在现代经济学的研究中具有重要地位。本文从随机广义Nash均衡的角度来分析电商领域中的实际问题,将电商领域...随着新时代的蓬勃发展,电商领域取得了历史性突破,但也伴随着许多不确定性问题显现。随机广义Nash均衡是非合作博弈的重要概念,在现代经济学的研究中具有重要地位。本文从随机广义Nash均衡的角度来分析电商领域中的实际问题,将电商领域中的问题等价于对应的随机广义Nash均衡问题。同时,采用样本平均近似法(SAA)处理随机因素,利用Nikaido-Isoda函数和改进的差分进化算法进行求解。最后,给出一个关于电商平台对应生产厂商产品生产数量问题的实例。结果显示,利用随机广义Nash均衡和差分进化算法来解决电商领域中的实际问题具有可行性,对电商平台的进一步发展具有研究意义。With the booming development of the new era, the field of e-commerce has made a historic breakthrough, but it is also accompanied by many revealed uncertainty problems. Stochastic Generalized Nash Equilibrium is an important concept of non-cooperative game, which occupies an important position in the study of modern economics. In this paper, we analyze the practical problems in the field of e-commerce from the perspective of Stochastic Generalized Nash Equilibrium, and equate the problems in the field of e-commerce with the corresponding Stochastic Generalized Nash Equilibrium problems. Meanwhile, the Sample Average Approximation (SAA) method is adopted to deal with the stochastic factors, and the Nikaido-Isoda function and the improved differential evolutionary algorithm are used for the solution. Finally, an example is given of the problem of the number of products produced by the corresponding manufacturer of the e-commerce platform. The results show that it is possible to use stochastic generalized Nash equilibrium and differential evolution algorithms to solve practical problems in the field of e-commerce, which has research implications for the further development of e-commerce platforms.展开更多
文摘本文研究一类低秩矩阵优化问题,其中惩罚项为目标矩阵奇异值的l_(p)(0<p<1)正则函数.基于半阈值函数在稀疏/低秩恢复问题中的良好性能,本文提出奇异值半阈值(singular value half thresholding,SVHT)算法来求解l_(p)正则矩阵优化问题.SVHT算法的主要迭代利用了子问题的闭式解,但与现有算法不同,其本质上是对目标函数在当前点进行局部1/2近似,而不是局部线性或局部二次近似.通过构造目标函数的Lipschitz和非Lipschitz近似函数,本文证明了SVHT算法生成序列的任意聚点都是问题的一阶稳定点.在数值实验中,利用模拟数据和实际图像数据的低秩矩阵补全问题对SVHT算法进行测试.大量的数值结果表明,SVHT算法对低秩矩阵优化问题在速度、精度和鲁棒性等方面都表现优异.
文摘在许多经济模型中,决策者需要通过比较集值优化问题的目标函数来衡量支出以达到自身收益的最大。在电子商务视角下,本文讨论了有限理性下基于改进集的集合优化问题E-u-最小解集的Levitin-Polyak良定性和广义Levitin-Polyak良定性,并通过有限理性模型证明了该良定性的充分条件。此外,借助非线性分析的方法给出了集合优化问题(广义) Levitin-Polyak良定性的特征刻画。这些结果为电子商务在实际生活中的应用打下了夯实的理论基础。In many economic models, decision-makers need to measure expenditures by comparing the objective functions of set-valued optimization problems in order to achieve maximum benefit. Under the perspective of E-commerce, this paper studies the Levitin-Polyak well-posedness and generalized Levitin-Polyak well-posedness of E-u-minimal solution of set optimization problems under bounded rationality via improvement set. Furthermore, the sufficient condition of well-posedness is given by using a bounded rationality model. Besides, we obtain the characterization of (generalized) Levitin-Polyak well-posedness for the problem by utilizing nonlinear analysis method. These results have laid a solid theoretical foundation for the application of E-commerce in practical life.
文摘随着新时代的蓬勃发展,电商领域取得了历史性突破,但也伴随着许多不确定性问题显现。随机广义Nash均衡是非合作博弈的重要概念,在现代经济学的研究中具有重要地位。本文从随机广义Nash均衡的角度来分析电商领域中的实际问题,将电商领域中的问题等价于对应的随机广义Nash均衡问题。同时,采用样本平均近似法(SAA)处理随机因素,利用Nikaido-Isoda函数和改进的差分进化算法进行求解。最后,给出一个关于电商平台对应生产厂商产品生产数量问题的实例。结果显示,利用随机广义Nash均衡和差分进化算法来解决电商领域中的实际问题具有可行性,对电商平台的进一步发展具有研究意义。With the booming development of the new era, the field of e-commerce has made a historic breakthrough, but it is also accompanied by many revealed uncertainty problems. Stochastic Generalized Nash Equilibrium is an important concept of non-cooperative game, which occupies an important position in the study of modern economics. In this paper, we analyze the practical problems in the field of e-commerce from the perspective of Stochastic Generalized Nash Equilibrium, and equate the problems in the field of e-commerce with the corresponding Stochastic Generalized Nash Equilibrium problems. Meanwhile, the Sample Average Approximation (SAA) method is adopted to deal with the stochastic factors, and the Nikaido-Isoda function and the improved differential evolutionary algorithm are used for the solution. Finally, an example is given of the problem of the number of products produced by the corresponding manufacturer of the e-commerce platform. The results show that it is possible to use stochastic generalized Nash equilibrium and differential evolution algorithms to solve practical problems in the field of e-commerce, which has research implications for the further development of e-commerce platforms.
