Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving no...Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.展开更多
This study proposes a hybrid controller by combining a proportional-integral-derivative （PID） control and a model reference adaptive control （MRAC）, which named as PID ＋ MRAC controller. The convergence performan...This study proposes a hybrid controller by combining a proportional-integral-derivative （PID） control and a model reference adaptive control （MRAC）, which named as PID ＋ MRAC controller. The convergence performances of the PID control, MRAC, and hybrid PID ＋ MRAC are also compared. Through the simulation in Matlab, the results show that the convergence speed and performance of the MRAC and the PID ＋MRAC controller are better than those of the PID controller. In addition, the convergence performance of the hybrid control is better than that of the MRAC control.展开更多
Trust region methods with nonmonotone technique for unconstrained opti-mization problems are presented and analyzed. The convergence results are demonstratedfor the proposed algorithms even if the conditions are mild.
The warming of the Arctic Intermediate Water （AIW） is studied based on the analyses of hydro- graphic observations in the Canada Basin of the Arctic Ocean during 1985-2006. It is shown that how the anomalously warm ...The warming of the Arctic Intermediate Water （AIW） is studied based on the analyses of hydro- graphic observations in the Canada Basin of the Arctic Ocean during 1985-2006. It is shown that how the anomalously warm AIW spreads in the Canada Basin during the observation time through the analysis of the AIW temperature spatial distribution in different periods. The results indicate that by 2006, the entire Canada Basin has almost been covered by the warming AIW. In order to study interannual variability of the AIW in the Canada Basin, the Canada Basin is divided into five regions according to the bottom topography. From the interannual variation of AIW temperature in each region, it is shown that a cooling period follows after the warming event in upstream regions. At the Chukchi Abyssal Plain and Chukchi Plateau, upstream of the Arctic Circumpolar Boundary Current （ACBC） in the Canada Basin, the AIW temperature reached maximum and then started to fall respectively in 2000 and 2002. However, the AIW in the Canada Abyssal Plain and Beaufort Sea continues to warm monotonically until the year 2006. Furthermore, it is revealed that there is convergence of the AIW depth in the five different regions of the Canada Basin when the AIW warming occurs during observation time. The difference of AIW depth between the five regions of the Canada Basin is getting smaller and smaller, all approaching 410 m in recent years. The results show that depth convergence is related to the variation of AIW potential density in the Canada Basin.展开更多
This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infi...This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.展开更多
A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The s...A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.展开更多
Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new...Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.展开更多
In this study, the two-sided Empirical Bayes test （EBT） rules for the parameter of continuous one-parameter exponential family with contaminated data （errors in variables） are constructed by a deconvolution kernel...In this study, the two-sided Empirical Bayes test （EBT） rules for the parameter of continuous one-parameter exponential family with contaminated data （errors in variables） are constructed by a deconvolution kernel method. The asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence, which depends on two types of the error distribu- tions for the proposed EBT rules, are obtained under suitable con- ditions. Finally, an example about the main results of this paper is given.展开更多
We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accele...We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses.展开更多
We study the nonlinear SchrSdinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iψt＋△ψ＋Ф（ωt）｜ψ...We study the nonlinear SchrSdinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iψt＋△ψ＋Ф（ωt）｜ψ｜αψ＋iξ （ωt）ψ= 0. Under some conditions, we show that as ω→∞ , the solution ψω will locally converge to the solution of the averaged equation iψt＋△ψ＋Ф（ωt）｜ψ｜αψ＋iξ （ωt）ψ= 0 with the same initial condition in Lq（（0, T）, B-S/T,2） for all admissible pairs （q, r）, where T∈ （0, Tmax）. We also show that if the dissipation coefficient ξ0 large enough, then, ψω is global if w is sufficiently large and ψω converges to ψ in Lq（（0, ∞）, B-S/T,2）, for all admissible pairs （q, r）. In particular, our results hold for both subcritical and critical nonlinearities.展开更多
Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique s...Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10771040)Guangxi Science Foundation (Grant No. 0832052)Guangxi University for Nationalities Youth Foundation (Grant No. 2007QN24)
文摘Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.
文摘This study proposes a hybrid controller by combining a proportional-integral-derivative （PID） control and a model reference adaptive control （MRAC）, which named as PID ＋ MRAC controller. The convergence performances of the PID control, MRAC, and hybrid PID ＋ MRAC are also compared. Through the simulation in Matlab, the results show that the convergence speed and performance of the MRAC and the PID ＋MRAC controller are better than those of the PID controller. In addition, the convergence performance of the hybrid control is better than that of the MRAC control.
文摘Trust region methods with nonmonotone technique for unconstrained opti-mization problems are presented and analyzed. The convergence results are demonstratedfor the proposed algorithms even if the conditions are mild.
基金The National Natural Science Foundation of China under contract Nos 40631006 and 40876003the Polar Science Youth Innovational Foundation of China under contract No. 20080221the National Key Basic Research Program "973" of China under contract No. 2010CB950301
文摘The warming of the Arctic Intermediate Water （AIW） is studied based on the analyses of hydro- graphic observations in the Canada Basin of the Arctic Ocean during 1985-2006. It is shown that how the anomalously warm AIW spreads in the Canada Basin during the observation time through the analysis of the AIW temperature spatial distribution in different periods. The results indicate that by 2006, the entire Canada Basin has almost been covered by the warming AIW. In order to study interannual variability of the AIW in the Canada Basin, the Canada Basin is divided into five regions according to the bottom topography. From the interannual variation of AIW temperature in each region, it is shown that a cooling period follows after the warming event in upstream regions. At the Chukchi Abyssal Plain and Chukchi Plateau, upstream of the Arctic Circumpolar Boundary Current （ACBC） in the Canada Basin, the AIW temperature reached maximum and then started to fall respectively in 2000 and 2002. However, the AIW in the Canada Abyssal Plain and Beaufort Sea continues to warm monotonically until the year 2006. Furthermore, it is revealed that there is convergence of the AIW depth in the five different regions of the Canada Basin when the AIW warming occurs during observation time. The difference of AIW depth between the five regions of the Canada Basin is getting smaller and smaller, all approaching 410 m in recent years. The results show that depth convergence is related to the variation of AIW potential density in the Canada Basin.
基金supported by the Doctoral Scientific Research Funds of Anhui University(J10113190005)the Tian Yuan Foundation of China(11426031)
文摘This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.
基金supported by National Center for Mathematics and Interdisciplinary Sciences,CASNational Natural Science Foundation of China (Grant Nos. 60931002 and 91130019)
文摘A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201304 and 11371253)the Innovation Program of Shanghai Municipal Education Commission
文摘Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.
基金Supported by the Fundamental Research Funds for the Central Universities of China(2013-Ia-040)
文摘In this study, the two-sided Empirical Bayes test （EBT） rules for the parameter of continuous one-parameter exponential family with contaminated data （errors in variables） are constructed by a deconvolution kernel method. The asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence, which depends on two types of the error distribu- tions for the proposed EBT rules, are obtained under suitable con- ditions. Finally, an example about the main results of this paper is given.
基金The authors are grateful to Prof. Zhaojun Bai in University of Cali- fornia, Davis, and Prof. Carlos J. Garcia-Cervera in University of California, Santa Barbara for their helpful discussions. The authors are grateful to the editor and the referees for their valuable comments, which improves the quality of the paper greatly. Weiguo Gao is supported by the National Natural Science Foundation of China under grants 91330202, Special Funds for Major State Basic Research Projects of China （2015CB858560003）, and Shanghai Science and Technology Development Funds 13dz2260200 and 13511504300. Qun Gu acknowledges the financial support from China Scholarship Council （No. 2011610055）.
文摘We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses.
基金supported by the NSFC Grants 10601021 and 11475073
文摘We study the nonlinear SchrSdinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iψt＋△ψ＋Ф（ωt）｜ψ｜αψ＋iξ （ωt）ψ= 0. Under some conditions, we show that as ω→∞ , the solution ψω will locally converge to the solution of the averaged equation iψt＋△ψ＋Ф（ωt）｜ψ｜αψ＋iξ （ωt）ψ= 0 with the same initial condition in Lq（（0, T）, B-S/T,2） for all admissible pairs （q, r）, where T∈ （0, Tmax）. We also show that if the dissipation coefficient ξ0 large enough, then, ψω is global if w is sufficiently large and ψω converges to ψ in Lq（（0, ∞）, B-S/T,2）, for all admissible pairs （q, r）. In particular, our results hold for both subcritical and critical nonlinearities.
文摘Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).
