We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we ...We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we give a sufficient condition based on the restricted isometry property for the stable recovery of signals.The l_(1-2)minimization model of Yin-Lou-He is extended to the l_(1-q)minimization model.展开更多
This study adopts the Dantzig’s Simplex method to investigate optimization of sand casting parameters for optimum service performance. Some process variables and mechanical properties were adapted into the Simplex me...This study adopts the Dantzig’s Simplex method to investigate optimization of sand casting parameters for optimum service performance. Some process variables and mechanical properties were adapted into the Simplex method. Aluminium alloy samples were cast, machined and subjected to a series of mechanical tests. From the body of data collected, linear functions and constraint equations were formulated and employed in the Dantzig’s Simplex method for optimization of process parameters. The results showed that the Simplex method can be adapted for studying performance opti- mization of castings.展开更多
As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed...As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin's paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.展开更多
广义Dantzig选择器问题是解决参数估计的有效途径,其中任何范数都可以用于估计.本文采用对偶交替方向乘子法(dual Alternating Direction Method of Multipliers,简称dADMM)求解e_(1)范数,e_(2)范数和e_(∞)范数广义Dantzig选择器问题,...广义Dantzig选择器问题是解决参数估计的有效途径,其中任何范数都可以用于估计.本文采用对偶交替方向乘子法(dual Alternating Direction Method of Multipliers,简称dADMM)求解e_(1)范数,e_(2)范数和e_(∞)范数广义Dantzig选择器问题,并给出了dADMM的全局收敛性和局部线性收敛速度.数值试验验证了dADMM的有效性.展开更多
基金supported by the National Natural Science Foundation of China“Variable exponential function spaces on variable anisotropic Euclidean spaces and their applications”(12261083),“Harmonic analysis on affine symmetric spaces”(12161083).
文摘We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we give a sufficient condition based on the restricted isometry property for the stable recovery of signals.The l_(1-2)minimization model of Yin-Lou-He is extended to the l_(1-q)minimization model.
文摘This study adopts the Dantzig’s Simplex method to investigate optimization of sand casting parameters for optimum service performance. Some process variables and mechanical properties were adapted into the Simplex method. Aluminium alloy samples were cast, machined and subjected to a series of mechanical tests. From the body of data collected, linear functions and constraint equations were formulated and employed in the Dantzig’s Simplex method for optimization of process parameters. The results showed that the Simplex method can be adapted for studying performance opti- mization of castings.
基金supported by the National Natural Science Foundation of China under Grant Nos.11501354,11201499,11301309 and 714732802015 Shanghai Young Faculty Training Program under Grant No.A1A-6119-15-003
文摘As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin's paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.
文摘广义Dantzig选择器问题是解决参数估计的有效途径,其中任何范数都可以用于估计.本文采用对偶交替方向乘子法(dual Alternating Direction Method of Multipliers,简称dADMM)求解e_(1)范数,e_(2)范数和e_(∞)范数广义Dantzig选择器问题,并给出了dADMM的全局收敛性和局部线性收敛速度.数值试验验证了dADMM的有效性.
基金supported by the National Natural Science Foundation of China(10871013,10871217)the NaturalScience Foundation of Beijing(1072004)Research Fund of Chongqing Technology and Business University(20105609)
