In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the op...In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.展开更多
In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and red...In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and reduces population diversity.To address these challenges,we propose a novel algorithm named Constraint IntensityDriven Evolutionary Multitasking(CIDEMT),which employs a two-stage,tri-task framework to dynamically integrates problem structure and knowledge transfer.In the first stage,three cooperative tasks are designed to explore the Constrained Pareto Front(CPF),the Unconstrained Pareto Front(UPF),and theε-relaxed constraint boundary,respectively.A CPF-UPF relationship classifier is employed to construct a problem-type-aware evolutionary strategy pool.At the end of the first stage,each task selects strategies from this strategy pool based on the specific type of problem,thereby guiding the subsequent evolutionary process.In the second stage,while each task continues to evolve,aτ-driven knowledge transfer mechanism is introduced to selectively incorporate effective solutions across tasks.enhancing the convergence and feasibility of the main task.Extensive experiments conducted on 32 benchmark problems from three test suites(LIRCMOP,DASCMOP,and DOC)demonstrate that CIDEMT achieves the best Inverted Generational Distance(IGD)values on 24 problems and the best Hypervolume values(HV)on 22 problems.Furthermore,CIDEMT significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).These results confirm CIDEMT’s superiority in promoting convergence,diversity,and robustness in solving complex CMOPs.展开更多
The melting process of a phase change material(PCM) inside a capsule can be promising in the thermal management of spacecraft. Such spacecraft operate under various gravity conditions, but previous studies have mostly...The melting process of a phase change material(PCM) inside a capsule can be promising in the thermal management of spacecraft. Such spacecraft operate under various gravity conditions, but previous studies have mostly considered the influence of gravity conditions on the constrained melting process of a PCM and not on its unconstrained melting process. In this study, a numerical model was constructed to comprehensively analyze the constrained and unconstrained melting processes of a PCM inside a spherical capsule under low-gravity conditions. After validation, the model was then applied to investigating the effects of low-gravity conditions on the evolution of velocity, temperature, melt layer thickness, heat transfer, liquid fraction, and total melting time. For the unconstrained melting process, low-gravity conditions weaken buoyancy-driven natural convection and slow down the solid PCM downward trend, thereby limiting the melting rate. In addition, the melt layer thickness does not increase linearly with decreasing gravity. Specifically, the increase in melt layer thickness is smaller by about 1.06 mm when the gravity drops from 0.4g to 0.2g compared to when it drops from 0.2g to 0.1g. The local heat flux in the contact melting area gradually decreases with the reduction of gravity during the unconstrained melting process. During the constrained melting process, notable oscillations in the local heat flux were observed. Decreasing the gravity from g to 0g increased the total melting times of the constrained and unconstrained melting processes by 417% and 621%, respectively.展开更多
The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow fie...The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow field,resulting in expensive computational costs.To improve the efficiency of solving adjoint equations,we propose a physics-constrained graph neural networks for solving adjoint equations,named ADJ-PCGN.ADJ-PCGN establishes a mapping relationship between flow characteristics and adjoint vector based on data,serving as a replacement for the computationally expensive numerical solution of adjoint equations.A physics-based graph structure and message-passing mechanism are designed to endow its strong fitting and generalization capabilities.Taking transonic drag reduction and maximum lift-drag ratio of the airfoil as examples,results indicate that ADJ-PCGN attains a similar optimal shape as the classical direct adjoint loop method.In addition,ADJ-PCGN demonstrates strong generalization capabilities across different mesh topologies,mesh densities,and out-of-distribution conditions.It holds the potential to become a universal model for aerodynamic shape optimization involving states,geometries,and meshes.展开更多
In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical a...In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.展开更多
In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are reg...In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.展开更多
By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential pr...By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it.Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.展开更多
For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for s...For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.展开更多
A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrain...A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrainfollowing grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.展开更多
A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the m...A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the master algorithm are generated by only one quadratic programming, and its step\|size is always one, the directions of the auxiliary algorithm are new “second\|order” feasible descent. Under suitable assumptions,the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence.展开更多
The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are establi...Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.展开更多
Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The adva...Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.展开更多
This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-eliminat...This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.展开更多
Dear Editor,This letter addresses the formation control problem for constrained underactuated autonomous underwater vehicles (AUVs). The feasibility condition of the virtual control law is eliminated by introducing a ...Dear Editor,This letter addresses the formation control problem for constrained underactuated autonomous underwater vehicles (AUVs). The feasibility condition of the virtual control law is eliminated by introducing a nonlinear state dependence function (NSDF) that transforms the state of each AUV in the formation.展开更多
By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential ...By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it. Global and local superlinear/ quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.展开更多
Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectiv...Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.展开更多
In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence...In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.展开更多
The constrained global optimization problem being considered, a modified integral_level set method was illustrated based on Chew_Zheng's paper on Integral Global Optimization and (Wu's) paper on Implementable ...The constrained global optimization problem being considered, a modified integral_level set method was illustrated based on Chew_Zheng's paper on Integral Global Optimization and (Wu's) paper on Implementable Algorithm Convergence of Modified Integral_Level Set Method for Global Optimization Problem. It has two characters: 1) Each phase must construct a new function which has the same global optimal value as that of primitive objective function; 2) Comparing it with (Zheng's) method, solving level set procedure is avoided. An implementable algorithm also is given and it is proved that this algorithm is convergent.展开更多
In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradien...In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.展开更多
基金Supported by the National Natural Science Foundation of China(12071133)Natural Science Foundation of Henan Province(252300421993)Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110005)。
文摘In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.
基金supported by the National Natural Science Foundation of China under Grant No.61972040the Science and Technology Research and Development Project funded by China Railway Material Trade Group Luban Company.
文摘In a wide range of engineering applications,complex constrained multi-objective optimization problems(CMOPs)present significant challenges,as the complexity of constraints often hampers algorithmic convergence and reduces population diversity.To address these challenges,we propose a novel algorithm named Constraint IntensityDriven Evolutionary Multitasking(CIDEMT),which employs a two-stage,tri-task framework to dynamically integrates problem structure and knowledge transfer.In the first stage,three cooperative tasks are designed to explore the Constrained Pareto Front(CPF),the Unconstrained Pareto Front(UPF),and theε-relaxed constraint boundary,respectively.A CPF-UPF relationship classifier is employed to construct a problem-type-aware evolutionary strategy pool.At the end of the first stage,each task selects strategies from this strategy pool based on the specific type of problem,thereby guiding the subsequent evolutionary process.In the second stage,while each task continues to evolve,aτ-driven knowledge transfer mechanism is introduced to selectively incorporate effective solutions across tasks.enhancing the convergence and feasibility of the main task.Extensive experiments conducted on 32 benchmark problems from three test suites(LIRCMOP,DASCMOP,and DOC)demonstrate that CIDEMT achieves the best Inverted Generational Distance(IGD)values on 24 problems and the best Hypervolume values(HV)on 22 problems.Furthermore,CIDEMT significantly outperforms six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs).These results confirm CIDEMT’s superiority in promoting convergence,diversity,and robustness in solving complex CMOPs.
基金supported by the National Natural Science Foundation of China (Grant No.52376181)。
文摘The melting process of a phase change material(PCM) inside a capsule can be promising in the thermal management of spacecraft. Such spacecraft operate under various gravity conditions, but previous studies have mostly considered the influence of gravity conditions on the constrained melting process of a PCM and not on its unconstrained melting process. In this study, a numerical model was constructed to comprehensively analyze the constrained and unconstrained melting processes of a PCM inside a spherical capsule under low-gravity conditions. After validation, the model was then applied to investigating the effects of low-gravity conditions on the evolution of velocity, temperature, melt layer thickness, heat transfer, liquid fraction, and total melting time. For the unconstrained melting process, low-gravity conditions weaken buoyancy-driven natural convection and slow down the solid PCM downward trend, thereby limiting the melting rate. In addition, the melt layer thickness does not increase linearly with decreasing gravity. Specifically, the increase in melt layer thickness is smaller by about 1.06 mm when the gravity drops from 0.4g to 0.2g compared to when it drops from 0.2g to 0.1g. The local heat flux in the contact melting area gradually decreases with the reduction of gravity during the unconstrained melting process. During the constrained melting process, notable oscillations in the local heat flux were observed. Decreasing the gravity from g to 0g increased the total melting times of the constrained and unconstrained melting processes by 417% and 621%, respectively.
基金supported by the National Natural Science Foundation of China(Grant No.12272316).
文摘The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow field,resulting in expensive computational costs.To improve the efficiency of solving adjoint equations,we propose a physics-constrained graph neural networks for solving adjoint equations,named ADJ-PCGN.ADJ-PCGN establishes a mapping relationship between flow characteristics and adjoint vector based on data,serving as a replacement for the computationally expensive numerical solution of adjoint equations.A physics-based graph structure and message-passing mechanism are designed to endow its strong fitting and generalization capabilities.Taking transonic drag reduction and maximum lift-drag ratio of the airfoil as examples,results indicate that ADJ-PCGN attains a similar optimal shape as the classical direct adjoint loop method.In addition,ADJ-PCGN demonstrates strong generalization capabilities across different mesh topologies,mesh densities,and out-of-distribution conditions.It holds the potential to become a universal model for aerodynamic shape optimization involving states,geometries,and meshes.
基金supported by the National Natural Science Foundation of China(Nos.52401342 and 12572025)the Fundamental Research Funds for the Central Universities of China(Nos.D5000240076 and G2025KY05171)+1 种基金the Natural Science Basic Research Program of Shaanxi Province(No.2025JCYBMS-026)the Basic Research Programs of Taicang(No.TC2024JC36)。
文摘In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.
基金funded by National Nature Science Foundation of China(92266203)National Nature Science Foundation of China(52205278)+1 种基金Key Projects of Shijiazhuang Basic Research Program(241791077A)Central Guide Local Science and Technology Development Fund Project of Hebei Province(246Z1022G).
文摘In this paper,a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints,utilizing the Solid Isotropic Material with Penalization approach.Element densities are regulated through sensitivity filtering tomitigate numerical instabilities associatedwith stress concentrations.Ap-norm aggregation function is employed to globalize local stress constraints,and a normalization technique linearly weights strain energy and stress,transforming the multi-objective problem into a single-objective formulation.The sensitivity of the objective function with respect to design variables is rigorously derived.Three numerical examples are presented,comparing the optimized structures in terms of strain energy,mass,and stress across five different mathematical models with varying combinations of optimization objectives.The results validate the effectiveness and feasibility of the proposed method for achieving a balanced design between structural stiffness and strength.This approach offers a new perspective for future research on stiffness-strength coordinated structural optimization.
基金Project supported by the Teaching and Research Award Program for the Outstanding YoungTeachers in Higher Education Institutes of Munistry of Education, P.R.China
文摘By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it.Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.
基金The National Natural Science Foundation of China(No.10972151,11272227)
文摘For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.
基金supported by the National Key Research and Development Program of China (Grant Nos. 2017YFC1501901 and 2017YFA0603901)the Beijing Natural Science Foundation (Grant No. JQ18001)
文摘A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrainfollowing grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.
基金Supported by the National Natural Science Foundation of China(1 980 1 0 0 9) and by the Natural Sci-ence Foundation of Guangxi
文摘A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the master algorithm are generated by only one quadratic programming, and its step\|size is always one, the directions of the auxiliary algorithm are new “second\|order” feasible descent. Under suitable assumptions,the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence.
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
基金Project supported by the National Natural Science Foundation of China(No.11432010)the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)+2 种基金the 111Project of China(No.B07050)the Fundamental Research Funds for the Central Universities(No.310201401JCQ01001)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX201517)
文摘Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.
文摘Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.
基金supported by the National Natural Science Foundation of China(62073094)the Fundamental Research Funds for the Central Universities(3072024GH0404)
文摘Dear Editor,This letter addresses the formation control problem for constrained underactuated autonomous underwater vehicles (AUVs). The feasibility condition of the virtual control law is eliminated by introducing a nonlinear state dependence function (NSDF) that transforms the state of each AUV in the formation.
文摘By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities （BVIs） was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it. Global and local superlinear/ quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.
基金supported in part by the National Natural Science Foundation of China(62173255,62188101)Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)
文摘Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.
文摘In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.
文摘The constrained global optimization problem being considered, a modified integral_level set method was illustrated based on Chew_Zheng's paper on Integral Global Optimization and (Wu's) paper on Implementable Algorithm Convergence of Modified Integral_Level Set Method for Global Optimization Problem. It has two characters: 1) Each phase must construct a new function which has the same global optimal value as that of primitive objective function; 2) Comparing it with (Zheng's) method, solving level set procedure is avoided. An implementable algorithm also is given and it is proved that this algorithm is convergent.
基金Supported by the Science and Technology Project of Guangxi(Guike AD23023002)。
文摘In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.
