In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorith...In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.展开更多
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
In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn （f, qn ;x） approximating to f＇ （x） as n →∞, which is a general- ization of that relating the classic...In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn （f, qn ;x） approximating to f＇ （x） as n →∞, which is a general- ization of that relating the classical case qn = 1. On the other hand, we study the conver- gence properties of derivatives of the limit q-Bernstein operators B∞（f, q;x） as q→1-.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
The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, ...The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments.展开更多
The purpose of this paper is to introduce a split generalized mixed equi- librium problem （SGMEP） and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its i...The purpose of this paper is to introduce a split generalized mixed equi- librium problem （SGMEP） and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its image un- der a given bounded linear operator is a solution of another generalized mixed equilibrium problem. We obtain some weak and strong convergence theorems.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
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
基金Supported by CERG: CityU 101005 of the Government of Hong Kong SAR, Chinathe National Natural ScienceFoundation of China, the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No.20040319003)the Natural Science Fund of Jiangsu Province of China (Grant No. BK2006214)
文摘In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.
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.
文摘In the present paper, we obtain estimations of convergence rate derivatives of the q-Bernstein polynomials Bn （f, qn ;x） approximating to f＇ （x） as n →∞, which is a general- ization of that relating the classical case qn = 1. On the other hand, we study the conver- gence properties of derivatives of the limit q-Bernstein operators B∞（f, q;x） as q→1-.
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).
基金supported by the National Natural Science Foundation of China (Grant Nos. 10471074, 10771116)the Doctoral Program of the Ministry of Education of China (Grant No. 20060003003)
文摘The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. Under certain condition, the method was proved to converge quadratically in literature. However, it is shown in this paper that under the original given condition the inexact RQI may not quadratically converge to the desired eigenpair and even may misconverge to some other undesired eigenpair. A new condition, called the uniform positiveness condition, is given that can fix misconvergence problem and ensure the quadratic convergence of the inexact RQI. An alternative to the inexact RQI is the Jacobi-Davidson (JD) method without subspace acceleration. A new proof of its linear convergence is presented and a sharper bound is established in the paper. All the results are verified and analyzed by numerical experiments.
基金supported by the Science and Technology Project of Education Department of Fujian Province(Grant number:JA13363)
文摘The purpose of this paper is to introduce a split generalized mixed equi- librium problem （SGMEP） and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its image un- der a given bounded linear operator is a solution of another generalized mixed equilibrium problem. We obtain some weak and strong convergence theorems.
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.
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.
