We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and e...We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy;2) an effective global search heuristic;and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.展开更多
Over the past few decades, numerous optimization-based methods have been proposed for solving the classification problem in data mining. Classic optimization-based methods do not consider attribute interactions toward...Over the past few decades, numerous optimization-based methods have been proposed for solving the classification problem in data mining. Classic optimization-based methods do not consider attribute interactions toward classification. Thus, a novel learning machine is needed to provide a better understanding on the nature of classification when the interaction among contributions from various attributes cannot be ignored. The interactions can be described by a non-additive measure while the Choquet integral can serve as the mathematical tool to aggregate the values of attributes and the corresponding values of a non-additive measure. As a main part of this research, a new nonlinear classification method with non-additive measures is proposed. Experimental results show that applying non-additive measures on the classic optimization-based models improves the classification robustness and accuracy compared with some popular classification methods. In addition, motivated by well-known Support Vector Machine approach, we transform the primal optimization-based nonlinear classification model with the signed non-additive measure into its dual form by applying Lagrangian optimization theory and Wolfes dual programming theory. As a result, 2n – 1 parameters of the signed non-additive measure can now be approximated with m (number of records) Lagrangian multipliers by applying necessary conditions of the primal classification problem to be optimal. This method of parameter approximation is a breakthrough for solving a non-additive measure practically when there are relatively small number of training cases available (mn-1). Furthermore, the kernel-based learning method engages the nonlinear classifiers to achieve better classification accuracy. The research produces practically deliverable nonlinear models with the non-additive measure for classification problem in data mining when interactions among attributes are considered.展开更多
Tow different computer calculation methods for distortion of the wide-band diode bridge track and hold amplifier (THA) are presented based on a high frequency Schottky diode model. One of the computer programs calcula...Tow different computer calculation methods for distortion of the wide-band diode bridge track and hold amplifier (THA) are presented based on a high frequency Schottky diode model. One of the computer programs calculates the distortion of weekly nonlinear THA based on the KCL and the nonlinear-current method. The other calculates the weekly nonlinear distortion by using a Volterra series method and a nodal formulation. Comparative calculation results for the diode bridge THA have shown good agreement with these two computer program calculation methods, whereas the overall computational efficiency of the nonlinear-current method is better than that of the nodal formulation method in a special evaluation.展开更多
文摘We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy;2) an effective global search heuristic;and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.
文摘Over the past few decades, numerous optimization-based methods have been proposed for solving the classification problem in data mining. Classic optimization-based methods do not consider attribute interactions toward classification. Thus, a novel learning machine is needed to provide a better understanding on the nature of classification when the interaction among contributions from various attributes cannot be ignored. The interactions can be described by a non-additive measure while the Choquet integral can serve as the mathematical tool to aggregate the values of attributes and the corresponding values of a non-additive measure. As a main part of this research, a new nonlinear classification method with non-additive measures is proposed. Experimental results show that applying non-additive measures on the classic optimization-based models improves the classification robustness and accuracy compared with some popular classification methods. In addition, motivated by well-known Support Vector Machine approach, we transform the primal optimization-based nonlinear classification model with the signed non-additive measure into its dual form by applying Lagrangian optimization theory and Wolfes dual programming theory. As a result, 2n – 1 parameters of the signed non-additive measure can now be approximated with m (number of records) Lagrangian multipliers by applying necessary conditions of the primal classification problem to be optimal. This method of parameter approximation is a breakthrough for solving a non-additive measure practically when there are relatively small number of training cases available (mn-1). Furthermore, the kernel-based learning method engages the nonlinear classifiers to achieve better classification accuracy. The research produces practically deliverable nonlinear models with the non-additive measure for classification problem in data mining when interactions among attributes are considered.
文摘Tow different computer calculation methods for distortion of the wide-band diode bridge track and hold amplifier (THA) are presented based on a high frequency Schottky diode model. One of the computer programs calculates the distortion of weekly nonlinear THA based on the KCL and the nonlinear-current method. The other calculates the weekly nonlinear distortion by using a Volterra series method and a nodal formulation. Comparative calculation results for the diode bridge THA have shown good agreement with these two computer program calculation methods, whereas the overall computational efficiency of the nonlinear-current method is better than that of the nodal formulation method in a special evaluation.
