An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are mad...An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.展开更多
By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by...By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.展开更多
The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing...The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.展开更多
For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator（QUEST） measurement noise model are complicated for just two observations. In our application, the mag...For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator（QUEST） measurement noise model are complicated for just two observations. In our application, the magnetometer and accelerometer are not two comparable kinds of sensors and both are not small field-of-view sensors as well. So in this paper a new unit measurement model is derived. According to the Wahba problem, the optimal weights for each measurement are obtained by the error variance researches. Then an improved quaternion Gauss–Newton method is presented and adopted to acquire attitude. Eventually, simulation results and experimental validation employed to test the proposed method demonstrate the usefulness of the improved algorithm.展开更多
In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link ca...In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link capacity improvements by maximizing net economic benefit while considering changes in demand and traffic distribution in network. The derivatives of equilibrium link flows and objective function with respect to capacity expansion variables, which are analytically derived, can be computed without having to first find path choice information. These derivatives are employed to develop a quasi Newton algorithm with the BFG S (Broyden- Fletcher- Goldfarb-Shanno) formula for solving the nonlinear, nonconvex but differentiable SUE-constrained network design problem. The SUE assignment with elastic demand is solved by using the method of successive averages in conjunction with Bell’s matrix inversion logit assignment method. Simple and complex example networks are presented to illustrate the model and the algorithm.展开更多
The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. ...The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.展开更多
Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-c...Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.展开更多
The stability of the Newton-like algorithm in optimization flow control is considered in this paper. This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theor...The stability of the Newton-like algorithm in optimization flow control is considered in this paper. This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theory,without considering the round trip time of each source. While the stability of this algorithm with considering the round trip time is analyzed as well. The analysis shows that the algorithm with only one bottleneck link accessed by several sources is also globally stable,and all trajectories described by this algorithm ultimately converge to the equilibrium point.展开更多
Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability...Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability. In this paper, we propose to inject distributed power generation into a distribution system while minimizing active energy losses. This injection should be done at a grid node (which is a point where energy can be injected into or recovered from the grid) that will be considered the optimal node when total active losses in the radial distribution system are minimal. The focus is on meeting energy demand using renewable energy sources. The main criterion is the minimization of active energy losses during injection. The method used is the algorithm of bee colony (ABC) associated with Newtonian energy flow transfer equations. The method has been implemented in MATLAB for optimal node search in IEEE 14, 33 and 57 nodes networks. The active energy loss results of this hybrid algorithm were compared with the results of previous searches. This comparison shows that the proposed algorithm allows to have reduced losses with the power injected that we have found.展开更多
In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinea...In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.展开更多
基金Project (2002CB312200) supported by the National Key Basic Research and Development Program of China Project(03JJY3109) supported by the Natural Science Foundation of Hunan Province
文摘An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.
基金Supported by China Postdoctoral Science Foundation(No.20060390660)Science and Technology Development Plan of Tianjin(No.06YFGZGX05600)+1 种基金Scientific Research Foundation of Liu Hui Center for Applied MathematicsNankai University-Tianjin University.
文摘By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption.
基金Supported by LIU Hui Centre for Applied Mathematics of Nankai University and Tianjin University
文摘The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.
文摘For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator（QUEST） measurement noise model are complicated for just two observations. In our application, the magnetometer and accelerometer are not two comparable kinds of sensors and both are not small field-of-view sensors as well. So in this paper a new unit measurement model is derived. According to the Wahba problem, the optimal weights for each measurement are obtained by the error variance researches. Then an improved quaternion Gauss–Newton method is presented and adopted to acquire attitude. Eventually, simulation results and experimental validation employed to test the proposed method demonstrate the usefulness of the improved algorithm.
基金Huang gratefully acknowledges the National Natural Science Foundation of China(Grant No. 79825001)and the Ministry of Educatio
文摘In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link capacity improvements by maximizing net economic benefit while considering changes in demand and traffic distribution in network. The derivatives of equilibrium link flows and objective function with respect to capacity expansion variables, which are analytically derived, can be computed without having to first find path choice information. These derivatives are employed to develop a quasi Newton algorithm with the BFG S (Broyden- Fletcher- Goldfarb-Shanno) formula for solving the nonlinear, nonconvex but differentiable SUE-constrained network design problem. The SUE assignment with elastic demand is solved by using the method of successive averages in conjunction with Bell’s matrix inversion logit assignment method. Simple and complex example networks are presented to illustrate the model and the algorithm.
基金supported in part by the National Outstanding Youth Foundation of P.R.China (60525303)the National Natural Science Foundation of P.R.China(60404022,60604004)+2 种基金the Natural Science Foundation of Hebei Province (102160)the special projects in mathematics funded by the Natural Science Foundation of Hebei Province(07M005)the NS of Education Office in Hebei Province (2004123).
文摘The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.
文摘Based on the extraction equilibrium and mass balances in countercurrent extraction systems, a novel method was studied for dealing with the extraction equilibrium and the mass distribution in a multi-component(gamma-component) system. The relationships of mass distribution (x(i), y(i), i = 1, ..., lambda) between two phases were expressed by 2 lambda dimensional simultaneous equations. These simultaneous equations can be converted to a one-dimension nonlinear equation, then it was solved by Newton-Raphson algorithm within a few number of iteration. Compared with the regular calculation method for the 2 lambda dimensional simultaneous equations, Newton-Raphson algorithm can decrease the number of iteration, increase the convergence of the equations and accelerate the speed of simulation. It was verified in many multi-component systems with satisfactory results. As an example, a five-component system is demonstrated in this paper.
基金the National Outstanding Youth Foundation of China (Grant No.60525303)the NNSF of China( Grant No.60404022 and 60604004)+2 种基金the NSF of Hebei Province (Grant No.102160)the Special Projects in Mathematics Funded by Natural Science Foundation of Hebei Prov-ince(Grant No.07M005)the NS of Education Office in Hebei Province (Grant No.2004123).
文摘The stability of the Newton-like algorithm in optimization flow control is considered in this paper. This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theory,without considering the round trip time of each source. While the stability of this algorithm with considering the round trip time is analyzed as well. The analysis shows that the algorithm with only one bottleneck link accessed by several sources is also globally stable,and all trajectories described by this algorithm ultimately converge to the equilibrium point.
文摘Distributed generation (DG) is gaining in importance due to the growing demand for electrical energy and the key role it plays in reducing actual energy losses, lowering operating costs and improving voltage stability. In this paper, we propose to inject distributed power generation into a distribution system while minimizing active energy losses. This injection should be done at a grid node (which is a point where energy can be injected into or recovered from the grid) that will be considered the optimal node when total active losses in the radial distribution system are minimal. The focus is on meeting energy demand using renewable energy sources. The main criterion is the minimization of active energy losses during injection. The method used is the algorithm of bee colony (ABC) associated with Newtonian energy flow transfer equations. The method has been implemented in MATLAB for optimal node search in IEEE 14, 33 and 57 nodes networks. The active energy loss results of this hybrid algorithm were compared with the results of previous searches. This comparison shows that the proposed algorithm allows to have reduced losses with the power injected that we have found.
基金supported by National Foundation of Natural Science under the Grant 11071216
文摘In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.
