In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existen...In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existence of solutions near the time asymptotic states which are local Maxwellians and the optimal convergence rates are obtained. The method used here has its own advantage for this kind of studies because it does not involve the spectrum analysis of the corresponding linearized operator.展开更多
The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some condit...The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some conditions on initial data.展开更多
In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the conv...In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the LP-norm of the perturbation is bounded for some p ε [1, 6).展开更多
Based on the newly-developed element energy projection (EEP) method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite ele...Based on the newly-developed element energy projection (EEP) method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method (FEM) is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.展开更多
The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Househo...The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods.展开更多
In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic sys...In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.展开更多
This article concerded with a semiparametric generalized partial linear model (GPLM) with the type Ⅱ censored data. A sieve maximum likelihood estimator (MLE) is proposed to estimate the parameter component, allo...This article concerded with a semiparametric generalized partial linear model (GPLM) with the type Ⅱ censored data. A sieve maximum likelihood estimator (MLE) is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.展开更多
The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consis...The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate (1 + t)^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate (1 + t)^-1/4 which is slower than the rate (1 + t)^-3/4 for the compressible Navier-Stokes equations (NS). In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate (1 + t)^-3/4+ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.展开更多
The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data...The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l(R3) ∩ B˙ s 1,1 (R3) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t) 1 4 s 2 in L2 -norm, which is slower than the rate (1+t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t) 3 4 due to the cancellation effect from the interplay interaction of the charged particles.展开更多
In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the ...In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.展开更多
This paper proves the error reduction property (saturation property), convergence and optimality of an adaptive mixed finite element method (AMFEM) for the Poisson equation. In each step of AMFEM, the local refine...This paper proves the error reduction property (saturation property), convergence and optimality of an adaptive mixed finite element method (AMFEM) for the Poisson equation. In each step of AMFEM, the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations, depending only on the marking strategy, under some restriction of refinement. The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe (2006) and the quasi-orthogonality estimate proved by Chen, Holst, and Xu (2009). Numerical experiments fully confirm the theoretical analysis.展开更多
In this paper, we address one of the issues in the frequency assignment problem for cellular mobile networks in which we intend to minimize the interference levels when assigning frequencies from a limited frequency s...In this paper, we address one of the issues in the frequency assignment problem for cellular mobile networks in which we intend to minimize the interference levels when assigning frequencies from a limited frequency spectrum. In order to satisfy the increasing demand in such cellular mobile networks, we use a hybrid approach consisting of a Particle Swarm Optimization(PSO) combined with a Tabu Search(TS) algorithm. This approach takes both advantages of PSO efficiency in global optimization and TS in avoiding the premature convergence that would lead PSO to stagnate in a local minimum. Moreover, we propose a new efficient, simple, and inexpensive model for storing and evaluating solution's assignment. The purpose of this model reduces the solution's storage volume as well as the computations required to evaluate thesesolutions in comparison with the classical model. Our simulation results on the most known benchmarking instances prove the effectiveness of our proposed algorithm in comparison with previous related works in terms of convergence rate, the number of iterations, the solution storage volume and the running time required to converge to the optimal solution.展开更多
Accelerating the convergence speed and avoiding the local optimal solution are two main goals of particle swarm optimization(PSO). The very basic PSO model and some variants of PSO do not consider the enhancement of...Accelerating the convergence speed and avoiding the local optimal solution are two main goals of particle swarm optimization(PSO). The very basic PSO model and some variants of PSO do not consider the enhancement of the explorative capability of each particle. Thus these methods have a slow convergence speed and may trap into a local optimal solution. To enhance the explorative capability of particles, a scheme called explorative capability enhancement in PSO(ECE-PSO) is proposed by introducing some virtual particles in random directions with random amplitude. The linearly decreasing method related to the maximum iteration and the nonlinearly decreasing method related to the fitness value of the globally best particle are employed to produce virtual particles. The above two methods are thoroughly compared with four representative advanced PSO variants on eight unimodal and multimodal benchmark problems. Experimental results indicate that the convergence speed and solution quality of ECE-PSO outperform the state-of-the-art PSO variants.展开更多
A new hybrid MMA-MGCMMA (HMM) algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version...A new hybrid MMA-MGCMMA (HMM) algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.展开更多
A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium w...A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.展开更多
BP is a commonly used neural network training method, which has some disadvantages, such as local minima, sensitivity of initial value of weights, total dependence on gradient information. This paper presents some met...BP is a commonly used neural network training method, which has some disadvantages, such as local minima, sensitivity of initial value of weights, total dependence on gradient information. This paper presents some methods to train a neural network, including standard particle swarm optimizer (PSO), guaranteed convergence particle swarm optimizer (GCPSO), an improved PSO algorithm, and GCPSO-BP, an algorithm combined GCPSO with BP. The simulation results demonstrate the effectiveness of the three algorithms for neural network training.展开更多
We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove ...We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.展开更多
In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes flows.In the mixed formulation,the unknowns are strain rate,stress and velocity,which a...In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes flows.In the mixed formulation,the unknowns are strain rate,stress and velocity,which are approximated by a discontinuous piecewise polynomial triplet ■for k≥0.Here,the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric.In addition,the pressure is easily recovered through simple postprocessing.For the benefit of the analysis,we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate,so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis.For k≥0,we get the optimal convergence order for the stress in broken ■(div)-norm and velocity in L^(2)-norm.Furthermore,the error estimates of the strain rate and the stress in-norm,and the pressure in L^(2)-norm are optimal under certain conditions.Finally,several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results.Numerical evidence is provided to show that the orders of convergence are sharp.展开更多
In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution w...In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model areremoved, and the mild conditions are obtained to guarantee the optimal rates of the estimatorof autoregression function. In addition, the strongly consistent estimator of the variance ofwhite noise is also constructed.展开更多
Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods p...Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing's work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations), the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.展开更多
基金supported by Strategic Research Grant of City University of Hong Kong, 7002129the Changjiang Scholar Program of Chinese Educational Ministry in Shanghai Jiao Tong University+1 种基金The research of the second author was supported partially by NSFC (10601018)partially by FANEDD
文摘In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existence of solutions near the time asymptotic states which are local Maxwellians and the optimal convergence rates are obtained. The method used here has its own advantage for this kind of studies because it does not involve the spectrum analysis of the corresponding linearized operator.
基金the first author is supported by the National Natural Science Foundation of China (11101188)the second author is supported by the National Natural Science Foundation of China (10871082)supported by the Fundamental Research Funds for the Central Universities
文摘The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some conditions on initial data.
基金supported by the National Natural Science Foundation of China(Nos.11071057 and 11271052)the Special Fund Project of Mathematical Tian Yuan Fund(No.11226029)
文摘In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the LP-norm of the perturbation is bounded for some p ε [1, 6).
基金the National Natural Science Foundation of China(No.50678093)Program for Changjiang Scholars and Innovative Research Team in University(No.IRT00736)
文摘Based on the newly-developed element energy projection (EEP) method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method (FEM) is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
基金This research was supported by Universiti Kebangsaan Malaysia under research grant GUP-2019-033.
文摘The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods.
基金Supported by National Natural Science Foundation of China-NSAF(10976026)the Research Funds for the Huaqiao Universities(12BS232)
文摘In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.
基金The talent research fund launched (3004-893325) of Dalian University of Technologythe NNSF (10271049) of China.
文摘This article concerded with a semiparametric generalized partial linear model (GPLM) with the type Ⅱ censored data. A sieve maximum likelihood estimator (MLE) is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.
基金The research of the first author was partially supported by the NNSFC No.10871134the NCET support of the Ministry of Education of China+4 种基金the Huo Ying Dong Fund No.111033the Chuang Xin Ren Cai Project of Beijing Municipal Commission of Education #PHR201006107the Instituteof Mathematics and Interdisciplinary Science at CNUThe research of the second author was supported by the General Research Fund of Hong Kong (CityU 103109)the National Natural Science Foundation of China,10871082
文摘The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate (1 + t)^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate (1 + t)^-1/4 which is slower than the rate (1 + t)^-3/4 for the compressible Navier-Stokes equations (NS). In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate (1 + t)^-3/4+ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.
基金supported by NSFC (10872004)National Basic Research Program of China (2010CB731500)the China Ministry of Education (200800010013)
文摘The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l(R3) ∩ B˙ s 1,1 (R3) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t) 1 4 s 2 in L2 -norm, which is slower than the rate (1+t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t) 3 4 due to the cancellation effect from the interplay interaction of the charged particles.
文摘In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.
基金supported in part by the Natural Science Foundation of China under Grant No.10771150the National Basic Research Program of China under Grant No.2005CB321701the Natural Science Foundation of Chongqing City under Grant No.CSTC,2010BB8270
文摘This paper proves the error reduction property (saturation property), convergence and optimality of an adaptive mixed finite element method (AMFEM) for the Poisson equation. In each step of AMFEM, the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations, depending only on the marking strategy, under some restriction of refinement. The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe (2006) and the quasi-orthogonality estimate proved by Chen, Holst, and Xu (2009). Numerical experiments fully confirm the theoretical analysis.
文摘In this paper, we address one of the issues in the frequency assignment problem for cellular mobile networks in which we intend to minimize the interference levels when assigning frequencies from a limited frequency spectrum. In order to satisfy the increasing demand in such cellular mobile networks, we use a hybrid approach consisting of a Particle Swarm Optimization(PSO) combined with a Tabu Search(TS) algorithm. This approach takes both advantages of PSO efficiency in global optimization and TS in avoiding the premature convergence that would lead PSO to stagnate in a local minimum. Moreover, we propose a new efficient, simple, and inexpensive model for storing and evaluating solution's assignment. The purpose of this model reduces the solution's storage volume as well as the computations required to evaluate thesesolutions in comparison with the classical model. Our simulation results on the most known benchmarking instances prove the effectiveness of our proposed algorithm in comparison with previous related works in terms of convergence rate, the number of iterations, the solution storage volume and the running time required to converge to the optimal solution.
基金supported by the Aeronautical Science Fund of Shaanxi Province of China(20145596025)
文摘Accelerating the convergence speed and avoiding the local optimal solution are two main goals of particle swarm optimization(PSO). The very basic PSO model and some variants of PSO do not consider the enhancement of the explorative capability of each particle. Thus these methods have a slow convergence speed and may trap into a local optimal solution. To enhance the explorative capability of particles, a scheme called explorative capability enhancement in PSO(ECE-PSO) is proposed by introducing some virtual particles in random directions with random amplitude. The linearly decreasing method related to the maximum iteration and the nonlinearly decreasing method related to the fitness value of the globally best particle are employed to produce virtual particles. The above two methods are thoroughly compared with four representative advanced PSO variants on eight unimodal and multimodal benchmark problems. Experimental results indicate that the convergence speed and solution quality of ECE-PSO outperform the state-of-the-art PSO variants.
基金This project is supported by National Basic Research Program of China(973Program, No.2003CB716207) and National Hi-tech Research and DevelopmentProgram of China(863 Program, No.2003AA001031).
文摘A new hybrid MMA-MGCMMA (HMM) algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.
基金Project supported by the Major State Basic Research Program of China (No. 19990328)the National Tackling Key Problems Program (No. 20050200069)+4 种基金the National Natural Science Foundation of China (Nos. 10771124, 10372052, 11101244, and 11271231)the Doctorate Foundation of the Ministry of Education of China (No. 20030422047)the Shandong Province Natural Science Foundation (No. ZR2009AQ012)the Independent Innovation Foundation of Shandong University(No. 2010TS031)the Scientific Research Award Fund for Excellent Middle-Aged and Young Scientists of Shandong Province (No. BS2009NJ003)
文摘A fractional step scheme with modified characteristic finite differences run- ning in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative commutation rule of differ- ence operators, multiplicative commutation rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in 12 norm is displayed to complete the convergence analysis of the numerical algo- rithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.
文摘BP is a commonly used neural network training method, which has some disadvantages, such as local minima, sensitivity of initial value of weights, total dependence on gradient information. This paper presents some methods to train a neural network, including standard particle swarm optimizer (PSO), guaranteed convergence particle swarm optimizer (GCPSO), an improved PSO algorithm, and GCPSO-BP, an algorithm combined GCPSO with BP. The simulation results demonstrate the effectiveness of the three algorithms for neural network training.
基金partly supported by the Institut Camille Jordan ST-Etienne Universitythe projects Argentine ANPCyT PICTO Austral 2008 # 73 and SOARD-AFOSR (No. FA9550-10-1-0023)
文摘We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.
基金supported by the National Natural Science Foundation of China(Grant No.12171383)the National Natural Science Foundation of China(Grant No.11971377).
文摘In this paper,we introduce and analyze an augmented mixed discontinuous Galerkin(MDG)method for a class of quasi-Newtonian Stokes flows.In the mixed formulation,the unknowns are strain rate,stress and velocity,which are approximated by a discontinuous piecewise polynomial triplet ■for k≥0.Here,the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric.In addition,the pressure is easily recovered through simple postprocessing.For the benefit of the analysis,we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate,so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis.For k≥0,we get the optimal convergence order for the stress in broken ■(div)-norm and velocity in L^(2)-norm.Furthermore,the error estimates of the strain rate and the stress in-norm,and the pressure in L^(2)-norm are optimal under certain conditions.Finally,several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results.Numerical evidence is provided to show that the orders of convergence are sharp.
文摘In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the or mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model areremoved, and the mild conditions are obtained to guarantee the optimal rates of the estimatorof autoregression function. In addition, the strongly consistent estimator of the variance ofwhite noise is also constructed.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)
文摘Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing's work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations), the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.