Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lips...Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.展开更多
In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region sub...In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved.Numerical results indicate that the new method is very efficient.展开更多
针对到达时间差/到达频率差(time difference of arrival/frequency difference of arrival,TDOA/FDOA)卫星干扰源定位系统中卫星速度难以准确预测,导致定位精度不高,尤其是在参考站数量较少时,定位误差较大的问题,提出了采用TDOA方法...针对到达时间差/到达频率差(time difference of arrival/frequency difference of arrival,TDOA/FDOA)卫星干扰源定位系统中卫星速度难以准确预测,导致定位精度不高,尤其是在参考站数量较少时,定位误差较大的问题,提出了采用TDOA方法实现高精度单参考站卫星干扰源定位。研究了TDOA卫星干扰源定位原理,建立了定位数学模型,采用信赖域算法计算干扰源的位置,进行了定位方法实验验证,分析了定位误差。通过对实测卫星信号的定位试验,证实了该定位方法在单参考站条件下显著提高卫星干扰源定位精度的有效性。展开更多
Surrogate-Based Optimization(SBO) is becoming increasingly popular since it can remarkably reduce the computational cost for design optimizations based on high-fidelity and expensive numerical analyses. However, for c...Surrogate-Based Optimization(SBO) is becoming increasingly popular since it can remarkably reduce the computational cost for design optimizations based on high-fidelity and expensive numerical analyses. However, for complicated optimization problems with a large design space, many design variables, and strong nonlinearity, SBO converges slowly and shows imperfection in local exploitation. This paper proposes a trust region method within the framework of an SBO process based on the Kriging model. In each refinement cycle, new samples are selected by a certain design of experiment method within a variable design space, which is sequentially updated by the trust region method. A multi-dimensional trust-region radius is proposed to improve the adaptability of the developed methodology. Further, the scale factor and the limit factor of the trust region are studied to evaluate their effects on the optimization process. Thereafter, different SBO methods using error-based exploration, prediction-based exploitation, refinement based on the expected improvement function, a hybrid refinement strategy, and the developed trust-regionbased refinement are utilized in four analytical tests. Further, the developed optimization methodology is employed in the drag minimization of an RAE2822 airfoil. Results indicate that it has better robustness and local exploitation capability in comparison with those of other SBO展开更多
文摘Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.
基金The authors would like to thank Prof Y.-X. Yuan for providing the source programsfor ref. [16]. Zhang Xiangsun was supported by the National Natural Science Foundation of China (Grant No. 39830070) Hong Kong Baptist University Zhang Juliang was su
文摘In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved.Numerical results indicate that the new method is very efficient.
文摘针对到达时间差/到达频率差(time difference of arrival/frequency difference of arrival,TDOA/FDOA)卫星干扰源定位系统中卫星速度难以准确预测,导致定位精度不高,尤其是在参考站数量较少时,定位误差较大的问题,提出了采用TDOA方法实现高精度单参考站卫星干扰源定位。研究了TDOA卫星干扰源定位原理,建立了定位数学模型,采用信赖域算法计算干扰源的位置,进行了定位方法实验验证,分析了定位误差。通过对实测卫星信号的定位试验,证实了该定位方法在单参考站条件下显著提高卫星干扰源定位精度的有效性。
基金co-supported by the National Natural Science Foundation of China (No. 11502209)the Free Research Projects of the Central University Funding of China (No. 3102015ZY007)
文摘Surrogate-Based Optimization(SBO) is becoming increasingly popular since it can remarkably reduce the computational cost for design optimizations based on high-fidelity and expensive numerical analyses. However, for complicated optimization problems with a large design space, many design variables, and strong nonlinearity, SBO converges slowly and shows imperfection in local exploitation. This paper proposes a trust region method within the framework of an SBO process based on the Kriging model. In each refinement cycle, new samples are selected by a certain design of experiment method within a variable design space, which is sequentially updated by the trust region method. A multi-dimensional trust-region radius is proposed to improve the adaptability of the developed methodology. Further, the scale factor and the limit factor of the trust region are studied to evaluate their effects on the optimization process. Thereafter, different SBO methods using error-based exploration, prediction-based exploitation, refinement based on the expected improvement function, a hybrid refinement strategy, and the developed trust-regionbased refinement are utilized in four analytical tests. Further, the developed optimization methodology is employed in the drag minimization of an RAE2822 airfoil. Results indicate that it has better robustness and local exploitation capability in comparison with those of other SBO
