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
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
Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with si...Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.展开更多
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ...In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.展开更多
An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H...An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.展开更多
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr...In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.展开更多
Accurate measurement of bean particle size is essential for automated grading and quality control in agricultural processing.However,existing image segmentation methods often suffer from low efficiency,over-segmentati...Accurate measurement of bean particle size is essential for automated grading and quality control in agricultural processing.However,existing image segmentation methods often suffer from low efficiency,over-segmentation,and high computational cost.We proposed a distancegradient dual constrained watershed algorithm for precise segmentation and measurement of bean particles.The method integrated distance transform-based seed extraction with gradient-constrained flooding,effectively suppressing noise-induced region fragmentation and improving the separation of adherent particles.An experimental platform was constructed using an industrial camera and an image-processing pipeline to evaluate performance.Compared with the conventional watershed algorithm,the proposed method improves segmentation accuracy by 7.2%and reduces the mean particle size error by 27.8%(0.13 mm,representing a relative error of 2.4%).Validation on three soybean varieties confirmed the robustness and generalizability of the approach.The results indicated that the proposed algorithm provided an efficient and accurate technique for agricultural particle size analysis,offering potential for integration into practical low-cost inspection systems.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.
基金supported by the National Natural Science Foundation of China(61202369)the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization(U1509219)
基金Project supported by the National Natural Science Foundation of China （Grant No. 10117733）, the Shanghai Leading Academic Discipline Project （Grant No.J50101）, and the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai （Grant No.06XPYQ52）
文摘Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.
文摘In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.
基金Project(2013CB035504)supported by the National Basic Research Program of China
文摘An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.
基金Supported by the Natural Science Foundation of Hubei Province (2008CDZD47)
文摘In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.
基金supported by National Natural Science Foundation of China(No.62006092)University Synergy Innovation Program of Anhui Province(No.GXXT-2023-108)Excellent Youth Project of Natural Science Research in Anhui Province(No.2023AH030081).
文摘Accurate measurement of bean particle size is essential for automated grading and quality control in agricultural processing.However,existing image segmentation methods often suffer from low efficiency,over-segmentation,and high computational cost.We proposed a distancegradient dual constrained watershed algorithm for precise segmentation and measurement of bean particles.The method integrated distance transform-based seed extraction with gradient-constrained flooding,effectively suppressing noise-induced region fragmentation and improving the separation of adherent particles.An experimental platform was constructed using an industrial camera and an image-processing pipeline to evaluate performance.Compared with the conventional watershed algorithm,the proposed method improves segmentation accuracy by 7.2%and reduces the mean particle size error by 27.8%(0.13 mm,representing a relative error of 2.4%).Validation on three soybean varieties confirmed the robustness and generalizability of the approach.The results indicated that the proposed algorithm provided an efficient and accurate technique for agricultural particle size analysis,offering potential for integration into practical low-cost inspection systems.
