One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, ...One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, we modifies a dual algorithm for constrained optimization problems and establishes a corresponding improved dual algorithm; It is proved that the improved dual algorithm has the local Q-superlinear convergence; Finally, we performed numerical experimentation using the improved dual algorithm for many constrained optimization problems, the numerical results are reported to show that it is valid in practical computation.展开更多
The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with ch...The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.展开更多
Variational image segmentation based on the Mumford and Shah model[31],together with implementation by the piecewise constant level-set method(PCLSM)[26],leads to fully nonlinear Total Variation(TV)-Allen-Cahn equatio...Variational image segmentation based on the Mumford and Shah model[31],together with implementation by the piecewise constant level-set method(PCLSM)[26],leads to fully nonlinear Total Variation(TV)-Allen-Cahn equations.The commonlyused numerical approaches usually suffer from the difficulties not only with the nondifferentiability of the TV-term,but also with directly evolving the discontinuous piecewise constant-structured solutions.In this paper,we propose efficient dual algorithms to overcome these drawbacks.The use of a splitting-penalty method results in TVAllen-Cahn type models associated with different"double-well"potentials,which allow for the implementation of the dual algorithm of Chambolle[8].Moreover,we present a new dual algorithm based on an edge-featured penalty of the dual variable,which only requires to solve a vectorial Allen-Cahn type equation with linear∇(div)-diffusion rather than fully nonlinear diffusion in the Chambolle’s approach.Consequently,more efficient numerical algorithms such as time-splitting method and Fast Fourier Transform(FFT)can be implemented.Various numerical tests show that two dual algorithms are much faster and more stable than the primal gradient descent approach,and the new dual algorithm is at least as efficient as the Chambolle’s algorithm but is more accurate.We demonstrate that the new method also provides a viable alternative for image restoration.展开更多
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simpl...Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.展开更多
We propose a slope-based decoupling algorithm to simultaneously control the dual deformable mirrors （DMs） in a woofer-tweeter adaptive optics system. This algorithm can directly use the woofer＇s response matrix mea...We propose a slope-based decoupling algorithm to simultaneously control the dual deformable mirrors （DMs） in a woofer-tweeter adaptive optics system. This algorithm can directly use the woofer＇s response matrix measured from a Shack-Hartmann wave-front sensor to construct a slope-based orthogonal basis, and then selectively distribute the large- amplitude low-order aberration to woofer DM and the remaining aberration to tweeter DM through the slope-based orthogonal basis. At the same moment, in order to avoid the two DMs generating opposite compensation, a constraint matrix used to reset tweeter control vector is convenient to be calculated with the slope-based orthogonal basis. Numeral simulation demonstrates that this algorithm has a good performance to control the adaptive optics system with dual DMs simultaneously. Compared with the typical decoupling algorithm, this algorithm can take full use of the compensation ability of woofer DM and release the stroke of tweeter DM to compensate high-order aberration. More importantly, it does not need to measure the accurate shape of tweeter＇s influence function and keeps better performance of restraining the coupling error with the continuous-dynamic aberration.展开更多
Modular inverse arithmetic plays an important role in elliptic curve cryptography. Based on the analysis of Montgomery modular inversion algorithm, this paper presents a new dual-field modular inversion algorithm, and...Modular inverse arithmetic plays an important role in elliptic curve cryptography. Based on the analysis of Montgomery modular inversion algorithm, this paper presents a new dual-field modular inversion algorithm, and a novel scalable and unified architecture for Montgomery inverse hardware in finite fields GF(p) and GF(2n) is proposed. Furthermore, this architecture based on the new modular inversion algorithm has been verified by modeling it in Verilog-HDL, and accomplished it under 0.18 μm CMOS technology. The result indicates that our work has better performance and flexibility than other works.展开更多
For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over th...For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.展开更多
A system reliability model based on Bayesian network(BN)is built via an evolutionary strategy called dual genetic algorithm(DGA).BN is a probabilistic approach to analyze relationships between stochastic events.In con...A system reliability model based on Bayesian network(BN)is built via an evolutionary strategy called dual genetic algorithm(DGA).BN is a probabilistic approach to analyze relationships between stochastic events.In contrast with traditional methods where BN model is built by professionals,DGA is proposed for the automatic analysis of historical data and construction of BN for the estimation of system reliability.The whole solution space of BN structures is searched by DGA and a more accurate BN model is obtained.Efficacy of the proposed method is shown by some literature examples.展开更多
Global navigation satellite system could provide accurate positioning results in signal complete condition. However, the performance is severe when signal denied, especially for the single-mode Bei Dou receiver. This ...Global navigation satellite system could provide accurate positioning results in signal complete condition. However, the performance is severe when signal denied, especially for the single-mode Bei Dou receiver. This paper proposes a dual-satellite positioning algorithm to promote the positioning performance in the satellite signal gap. The new algorithm utilizes the previous positioning data stored in complete condition to simplify the positioning equations. As the clock bias persists for a short period, this proposed method could work out accurate positioning results by only two visible satellites, without the need of computing the clock bias. Also, the Kalman filtering algorithm is used to smooth the trajectories, and improve the positioning results. During the incomplete period, only two satellites for 30 seconds and three satellites for 60 seconds, the preliminary experiment result shows that, the presented method could provide almost the same positioning results as in complete condition.展开更多
In this paper, two approaches are developed for directly identifying single-rate models of dual-rate stochastic systems in which the input updating frequency is an integer multiple of the output sampling frequency. Th...In this paper, two approaches are developed for directly identifying single-rate models of dual-rate stochastic systems in which the input updating frequency is an integer multiple of the output sampling frequency. The first is the generalized Yule-Walker algorithm and the second is a two-stage algorithm based on the correlation technique. The basic idea is to directly identify the parameters of underlying single-rate models instead of the lifted models of dual-rate systems from the dual-rate input-output data, assuming that the measurement data are stationary and ergodic. An example is given.展开更多
A major issue in radar quantitative precipitation estimation is the contamination of radar echoes by non-meteorological targets such as ground clutter,chaff,clear air echoes etc.In this study,a fuzzy logic algorithm f...A major issue in radar quantitative precipitation estimation is the contamination of radar echoes by non-meteorological targets such as ground clutter,chaff,clear air echoes etc.In this study,a fuzzy logic algorithm for the identification of non-meteorological echoes is developed using optimized membership functions and weights for the dual-polarization radar located at Mount Sobaek.For selected precipitation and non-meteorological events,the characteristics of the precipitation and non-meteorological echo are derived by the probability density functions of five fuzzy parameters as functions of reflectivity values.The membership functions and weights are then determined by these density functions.Finally,the nonmeteorological echoes are identified by combining the membership functions and weights.The performance is qualitatively evaluated by long-term rain accumulation.The detection accuracy of the fuzzy logic algorithm is calculated using the probability of detection（POD）,false alarm rate（FAR）,and clutter–signal ratio（CSR）.In addition,the issues in using filtered dual-polarization data are alleviated.展开更多
针对多目标狼群算法存在的搜索不充分、收敛性不足和多样性欠缺的问题,以及缺少对约束进行处理的问题,提出环境选择的双种群约束多目标狼群算法(multi-objective wolf pack algorithm for dual population constraints with environment...针对多目标狼群算法存在的搜索不充分、收敛性不足和多样性欠缺的问题,以及缺少对约束进行处理的问题,提出环境选择的双种群约束多目标狼群算法(multi-objective wolf pack algorithm for dual population constraints with environment selection,DCMOWPA-ES)。引入双种群约束处理方法给种群设置不同的搜索偏好,主种群运用可行性准则优先保留可行解,次种群通过ε约束探索不可行区域并将搜索结果传递给主种群,让算法能较好应对复杂的不可行区域,保障算法的可行性;提出维度选择的随机游走策略,使人工狼可自主选择游走方向,提高种群的全局搜索能力;设计精英学习的步长调整机制,人工狼通过向头狼学习的方式提升种群的局部搜索能力,确保算法的收敛性;采用环境选择的狼群更新策略,根据人工狼被支配的情况和所处位置的密度信息对其赋值,选择被支配数少且密度信息小的人工狼作为优秀个体,改善算法的多样性。为验证算法性能,将DCMOWPA-ES与六种新兴约束多目标优化算法在两组约束多目标测试集和汽车侧面碰撞设计问题上进行对比实验。实验结果表明,DCMOWPA-ES算法具备较好的可行性、收敛性和多样性。展开更多
基金Supported by the National 863 Project (2003AA002030)
文摘One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, we modifies a dual algorithm for constrained optimization problems and establishes a corresponding improved dual algorithm; It is proved that the improved dual algorithm has the local Q-superlinear convergence; Finally, we performed numerical experimentation using the improved dual algorithm for many constrained optimization problems, the numerical results are reported to show that it is valid in practical computation.
文摘The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.
基金supported by Singapore AcRF Tier 1 Grant RG58/08,Singapore MOE Grant T207B2202 and Singapore NRF2007IDM-IDM002-010.
文摘Variational image segmentation based on the Mumford and Shah model[31],together with implementation by the piecewise constant level-set method(PCLSM)[26],leads to fully nonlinear Total Variation(TV)-Allen-Cahn equations.The commonlyused numerical approaches usually suffer from the difficulties not only with the nondifferentiability of the TV-term,but also with directly evolving the discontinuous piecewise constant-structured solutions.In this paper,we propose efficient dual algorithms to overcome these drawbacks.The use of a splitting-penalty method results in TVAllen-Cahn type models associated with different"double-well"potentials,which allow for the implementation of the dual algorithm of Chambolle[8].Moreover,we present a new dual algorithm based on an edge-featured penalty of the dual variable,which only requires to solve a vectorial Allen-Cahn type equation with linear∇(div)-diffusion rather than fully nonlinear diffusion in the Chambolle’s approach.Consequently,more efficient numerical algorithms such as time-splitting method and Fast Fourier Transform(FFT)can be implemented.Various numerical tests show that two dual algorithms are much faster and more stable than the primal gradient descent approach,and the new dual algorithm is at least as efficient as the Chambolle’s algorithm but is more accurate.We demonstrate that the new method also provides a viable alternative for image restoration.
文摘Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.
基金Project supported by the Key Scientific Equipment Development Project of China(Grant No.ZDYZ2013-2)the National High-Tech R&D Program of China(Grant Nos.G128201-G158201 and G128603-G158603)+2 种基金the Innovation Fund of Chinese Academy of Science(Grant No.CXJJ-16M208)the Youth Innovation Promotion Association of the Chinese Academy of Sciencesthe Outstanding Young Scientists,Chinese Academy of Sciences
文摘We propose a slope-based decoupling algorithm to simultaneously control the dual deformable mirrors （DMs） in a woofer-tweeter adaptive optics system. This algorithm can directly use the woofer＇s response matrix measured from a Shack-Hartmann wave-front sensor to construct a slope-based orthogonal basis, and then selectively distribute the large- amplitude low-order aberration to woofer DM and the remaining aberration to tweeter DM through the slope-based orthogonal basis. At the same moment, in order to avoid the two DMs generating opposite compensation, a constraint matrix used to reset tweeter control vector is convenient to be calculated with the slope-based orthogonal basis. Numeral simulation demonstrates that this algorithm has a good performance to control the adaptive optics system with dual DMs simultaneously. Compared with the typical decoupling algorithm, this algorithm can take full use of the compensation ability of woofer DM and release the stroke of tweeter DM to compensate high-order aberration. More importantly, it does not need to measure the accurate shape of tweeter＇s influence function and keeps better performance of restraining the coupling error with the continuous-dynamic aberration.
基金Supported by the National High Technology Research and Development Program of China (863 Program) (No. 2008AA01Z103)
文摘Modular inverse arithmetic plays an important role in elliptic curve cryptography. Based on the analysis of Montgomery modular inversion algorithm, this paper presents a new dual-field modular inversion algorithm, and a novel scalable and unified architecture for Montgomery inverse hardware in finite fields GF(p) and GF(2n) is proposed. Furthermore, this architecture based on the new modular inversion algorithm has been verified by modeling it in Verilog-HDL, and accomplished it under 0.18 μm CMOS technology. The result indicates that our work has better performance and flexibility than other works.
基金supported by the National Natural Science Foundation of China (No. 61174126)
文摘For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.
基金National Natural Science Foundation of China(No.61203184)
文摘A system reliability model based on Bayesian network(BN)is built via an evolutionary strategy called dual genetic algorithm(DGA).BN is a probabilistic approach to analyze relationships between stochastic events.In contrast with traditional methods where BN model is built by professionals,DGA is proposed for the automatic analysis of historical data and construction of BN for the estimation of system reliability.The whole solution space of BN structures is searched by DGA and a more accurate BN model is obtained.Efficacy of the proposed method is shown by some literature examples.
基金partially supported by the National Natural Science Foundation of China under Grant No.61601296, 61601295, and 61671304
文摘Global navigation satellite system could provide accurate positioning results in signal complete condition. However, the performance is severe when signal denied, especially for the single-mode Bei Dou receiver. This paper proposes a dual-satellite positioning algorithm to promote the positioning performance in the satellite signal gap. The new algorithm utilizes the previous positioning data stored in complete condition to simplify the positioning equations. As the clock bias persists for a short period, this proposed method could work out accurate positioning results by only two visible satellites, without the need of computing the clock bias. Also, the Kalman filtering algorithm is used to smooth the trajectories, and improve the positioning results. During the incomplete period, only two satellites for 30 seconds and three satellites for 60 seconds, the preliminary experiment result shows that, the presented method could provide almost the same positioning results as in complete condition.
基金This work was supported by the National Natural Science Foundation of China (No. 60574051).
文摘In this paper, two approaches are developed for directly identifying single-rate models of dual-rate stochastic systems in which the input updating frequency is an integer multiple of the output sampling frequency. The first is the generalized Yule-Walker algorithm and the second is a two-stage algorithm based on the correlation technique. The basic idea is to directly identify the parameters of underlying single-rate models instead of the lifted models of dual-rate systems from the dual-rate input-output data, assuming that the measurement data are stationary and ergodic. An example is given.
基金supported by a grant(14AWMP-B079364-01) from Water Management Research Program funded by Ministry of Land,Infrastructure and Transport of Korean government
文摘A major issue in radar quantitative precipitation estimation is the contamination of radar echoes by non-meteorological targets such as ground clutter,chaff,clear air echoes etc.In this study,a fuzzy logic algorithm for the identification of non-meteorological echoes is developed using optimized membership functions and weights for the dual-polarization radar located at Mount Sobaek.For selected precipitation and non-meteorological events,the characteristics of the precipitation and non-meteorological echo are derived by the probability density functions of five fuzzy parameters as functions of reflectivity values.The membership functions and weights are then determined by these density functions.Finally,the nonmeteorological echoes are identified by combining the membership functions and weights.The performance is qualitatively evaluated by long-term rain accumulation.The detection accuracy of the fuzzy logic algorithm is calculated using the probability of detection（POD）,false alarm rate（FAR）,and clutter–signal ratio（CSR）.In addition,the issues in using filtered dual-polarization data are alleviated.
文摘针对多目标狼群算法存在的搜索不充分、收敛性不足和多样性欠缺的问题,以及缺少对约束进行处理的问题,提出环境选择的双种群约束多目标狼群算法(multi-objective wolf pack algorithm for dual population constraints with environment selection,DCMOWPA-ES)。引入双种群约束处理方法给种群设置不同的搜索偏好,主种群运用可行性准则优先保留可行解,次种群通过ε约束探索不可行区域并将搜索结果传递给主种群,让算法能较好应对复杂的不可行区域,保障算法的可行性;提出维度选择的随机游走策略,使人工狼可自主选择游走方向,提高种群的全局搜索能力;设计精英学习的步长调整机制,人工狼通过向头狼学习的方式提升种群的局部搜索能力,确保算法的收敛性;采用环境选择的狼群更新策略,根据人工狼被支配的情况和所处位置的密度信息对其赋值,选择被支配数少且密度信息小的人工狼作为优秀个体,改善算法的多样性。为验证算法性能,将DCMOWPA-ES与六种新兴约束多目标优化算法在两组约束多目标测试集和汽车侧面碰撞设计问题上进行对比实验。实验结果表明,DCMOWPA-ES算法具备较好的可行性、收敛性和多样性。
