In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac...In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.展开更多
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with...In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.展开更多
This paper proposes a scheme for the implementation of 1→ 3 optimal phase-covariant quantum cloning with trapped ions. In the present protocol, the required time for the whole procedure is short due to the resonant i...This paper proposes a scheme for the implementation of 1→ 3 optimal phase-covariant quantum cloning with trapped ions. In the present protocol, the required time for the whole procedure is short due to the resonant interaction, which is important in view of decoherence. Furthermore, the scheme is feasible based on current technologies.展开更多
0-1 programming is a special case of the integer programming, which is commonly encountered in many optimization problems. Neural network and its general energy function are presented for 0-1 optimization problem. The...0-1 programming is a special case of the integer programming, which is commonly encountered in many optimization problems. Neural network and its general energy function are presented for 0-1 optimization problem. Then, the 0-1 optimization problems are solved by a neural network model with transient chaotic dynamics (TCNN). Numerical simulations of two typical 0-1 optimization problems show that TCNN can overcome HNN's main drawbacks that it suffers from the local minimum and can search for the global optimal solutions in to solveing 0-1 optimization problems.展开更多
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
A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are ...A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.展开更多
This paper considers the geometric design of crab-like walkers and climbers, without decoupling leg design from overall machine design. Crab-like machines represent an important sub-class of multi-legged robots, bein...This paper considers the geometric design of crab-like walkers and climbers, without decoupling leg design from overall machine design. Crab-like machines represent an important sub-class of multi-legged robots, being particularly well suited to crossing difficult terrains. Firstly, the kinematic configurations and constraints are described, which determine the machine’s kinematic characteristics. The influence of the design parameters on the kinematic workspace is discussed. Finally, a two stage design methodology is presented, comprising kinematic design and design optimisation, the latter being based on the use of design maps rather than numerical optimisation. The performance measures considered during design optimisation include kinematic, static and quasi-static measures.展开更多
The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant ...The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and *-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.展开更多
The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaini...The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.展开更多
In this paper, we construct two models for the searching task for a lost plane. Model 1 determines the searching area. We predict the trajectory of floats generated after the disintegration of the plane by using RBF n...In this paper, we construct two models for the searching task for a lost plane. Model 1 determines the searching area. We predict the trajectory of floats generated after the disintegration of the plane by using RBF neural network model, and then determine the searching area according to the trajectory. With the pass of time, the searching area will also be constantly moving along the trajectory. Model 2 develops a maritime search plan to achieve the purpose of completing the search in the shortest time. We optimize the searching time and transform the problem into the 0-1 knapsack problem. Solving this problem by improved genetic algorithm, we can get the shortest searching time and the best choice for the search power.展开更多
Many economic problems can be formulated as optimization problems. Econometricians have long devoted their efforts to construct the econometric equation systems, while the corresponding objective functions receive few...Many economic problems can be formulated as optimization problems. Econometricians have long devoted their efforts to construct the econometric equation systems, while the corresponding objective functions receive few attentions. In recent twenty years, some techniques to construct the objective functions with economic implications have been developed, which might have a potential in economic decision-making. In the paper we app1y the method of constructing objective function to design an optimization model for monthly monetary planning of China. The real monthly data from l991 to l999 are used to evaluate the monthly economic situation. Our empirical experiment shows that the model gives a good short-term forecasting.展开更多
Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadrati...Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadratic serendipity element shape function is introduced from the linear generalized barycentric coordinates,and the quadratic serendipity element function space based on Wachspress coordinate is selected as the trial function space.Moreover,we construct a family of unified dual partitions for arbitrary convex polygonal meshes,which is crucial to finite volume element scheme,and propose a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom.Finally,under certain geometric assumption conditions,the optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained,and verified by numerical experiments.展开更多
Atrazine, a widely used herbicide, is increasing the agricultural production effectively, while also causing great environmental concern. Efficient atrazine-degrading bacterium is necessary to removal atrazine rapidly...Atrazine, a widely used herbicide, is increasing the agricultural production effectively, while also causing great environmental concern. Efficient atrazine-degrading bacterium is necessary to removal atrazine rapidly to keep a safe environment. In the present study, a new atrazine-degrading strain ZXY-1, identified as Pseudomonas, was isolated. This new isolated strain has a strong ability to biodegrade atrazine with a high efficiency of 9.09 mg/L/hr.Temperature, p H, inoculum size and initial atrazine concentration were examined to further optimize the degradation of atrazine, and the synthetic effect of these factors were investigated by the response surface methodology. With a high quadratic polynomial mathematical model(R^2= 0.9821) being obtained, the highest biodegradation efficiency of 19.03 mg/L/hr was reached compared to previous reports under the optimal conditions(30.71°C, pH 7.14, 4.23%(V/V) inoculum size and 157.1 mg/L initial atrazine concentration).Overall, this study provided an efficient bacterium and approach that could be potentially useful for the bioremediation of wastewater containing atrazine.展开更多
In the paper,we consider the l_(1)-regularized least square problem which has been intensively involved in the fields of signal processing,compressive sensing,linear inverse problems and statistical inference.The cons...In the paper,we consider the l_(1)-regularized least square problem which has been intensively involved in the fields of signal processing,compressive sensing,linear inverse problems and statistical inference.The considered problem has been proved recently to be equivalent to a nonnegatively constrained quadratic programming(QP).In this paper,we use a recently developed active conjugate gradient method to solve the resulting QP problem.To improve the algorithm’s performance,we design a subspace exact steplength as well as a precondition technique.The performance comparisons illustrate that the proposed algorithm is competitive and even performs little better than several state-of-the-art algorithms.展开更多
Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a problem of the in...Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a problem of the initial boundary values for a system of 3-dimensional nonlinear parabolic partial differential equations, one being the pressure flow equation and the other is the concentration convection-dispersion equation of the salt contained. For a generic case of a 3-dimensional bounded region, a backward-difference time-stepping scheme is defined. It approximates the pressure by the standard Galerkin procedure and the concentration by a Galerkin method of charederistics, where calculus of variations, theory of prior estimates and techniques are made use of Optimal order estimates in H1 norm are derived for the errors in the approximate solution.展开更多
With advantages of low costs and high energy density,Li–S batteries are considered as one of the most promising energy storage devices.However,Li_(2)S_(2) with a high dissociation energy and insulative properties is ...With advantages of low costs and high energy density,Li–S batteries are considered as one of the most promising energy storage devices.However,Li_(2)S_(2) with a high dissociation energy and insulative properties is hard to convert into Li_(2)S,resulting in underutilization of sulfur capacity.Herein,Co-Mo_(2)C@C yolk–shell spheres as nanoreactors were designed to confront this challenge rationally.The Co-Mo_(2)C@C-induced Li_(2)S_(1/2) nucleation and growth in the three-dimensional process and the cathode produced more Li_(2)S after full discharge.Experimental studies and theoretical calculations reveal that the conversion barrier from Li_(2)S_(2) into Li_(2)S was lowered while the diffusion of lithium ions and electron transfer accelerated when using the Co-Mo_(2)C@C catalyst.Based on the above advantages,the Co-Mo_(2)C@C/S cathode exhibits a high reversible capacity and excellent cyclic stability,such as an initial specific capacity of 1200 mAh g^(−1) at 0.1 C with 709 mAh g^(−1) at 1.0 C after 1000 cycles with a low capacity fading rate of 0.04%per cycle.Even at high densities of 3.0 C and 5.0 C,the specific capacities are 647.6 and 557.7 mAh g^(−1) after 400 cycles,respectively.Impressively,it also shows ca.770 and 900 mAh g^(−1) at 0.2 C after 50 cycles with high sulfur loadings of 4.2 and 5.1 mg cm−2,respectively.The present work may provide new insights into the design of nanoreactors to promote Li_(2)S_(1/2) growth in a three-dimensional process and accelerate conversion from solid Li_(2)S_(2) to solid Li_(2)S in high performance Li–S batteries.展开更多
文摘In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.
文摘In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
基金Project supported by the National Natural Science Foundation of China(Grant Nos10574022 and 10575022)the Funds of the Natural Science of Fujian Province,China(Grant Nos Z0512006 and A0210014)
文摘This paper proposes a scheme for the implementation of 1→ 3 optimal phase-covariant quantum cloning with trapped ions. In the present protocol, the required time for the whole procedure is short due to the resonant interaction, which is important in view of decoherence. Furthermore, the scheme is feasible based on current technologies.
基金This project was supported by the National Natural Science Foundation of China (79970042).
文摘0-1 programming is a special case of the integer programming, which is commonly encountered in many optimization problems. Neural network and its general energy function are presented for 0-1 optimization problem. Then, the 0-1 optimization problems are solved by a neural network model with transient chaotic dynamics (TCNN). Numerical simulations of two typical 0-1 optimization problems show that TCNN can overcome HNN's main drawbacks that it suffers from the local minimum and can search for the global optimal solutions in to solveing 0-1 optimization problems.
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Supported by National Natural Science Fund of China (11061021)Key Project of Chinese Ministry of Education (12024)+2 种基金Natural Science Fund of Inner Mongolia Autonomous Region (2012MS0108,2012MS0106,2011BS0102)Scientific Research Projection of Higher Schools of Inner Mongolia (NJZZ12011,NJZY13199)Program of Higher-level talents of Inner Mongolia University (125119,Z200901004,30105-125132)
文摘A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.
文摘This paper considers the geometric design of crab-like walkers and climbers, without decoupling leg design from overall machine design. Crab-like machines represent an important sub-class of multi-legged robots, being particularly well suited to crossing difficult terrains. Firstly, the kinematic configurations and constraints are described, which determine the machine’s kinematic characteristics. The influence of the design parameters on the kinematic workspace is discussed. Finally, a two stage design methodology is presented, comprising kinematic design and design optimisation, the latter being based on the use of design maps rather than numerical optimisation. The performance measures considered during design optimisation include kinematic, static and quasi-static measures.
基金supported by the National Natural Science Foundation of China (No.60774044)the Professional Research Foundation for Advanced Talents of Jiangsu University (No.07JDG037)+2 种基金the Natural Science Fund for Colleges and Universities in Jiangsu Province (No.08KJ510010)the Open Project of National Key Laboratory of Industrial Control Technology of Zhejiang University (No.ICT0910)Qing Lan Project of Jiangsu Province
文摘The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and *-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.
基金This project was supported by the National Nature Science Foundation of China (60374009)Nature Science Foundation of Guangdong Province of China (990795).
文摘The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.
文摘In this paper, we construct two models for the searching task for a lost plane. Model 1 determines the searching area. We predict the trajectory of floats generated after the disintegration of the plane by using RBF neural network model, and then determine the searching area according to the trajectory. With the pass of time, the searching area will also be constantly moving along the trajectory. Model 2 develops a maritime search plan to achieve the purpose of completing the search in the shortest time. We optimize the searching time and transform the problem into the 0-1 knapsack problem. Solving this problem by improved genetic algorithm, we can get the shortest searching time and the best choice for the search power.
基金The research is supported by National Natural Science Foundation of China (No. 79790l30 andNo. 70071045)
文摘Many economic problems can be formulated as optimization problems. Econometricians have long devoted their efforts to construct the econometric equation systems, while the corresponding objective functions receive few attentions. In recent twenty years, some techniques to construct the objective functions with economic implications have been developed, which might have a potential in economic decision-making. In the paper we app1y the method of constructing objective function to design an optimization model for monthly monetary planning of China. The real monthly data from l991 to l999 are used to evaluate the monthly economic situation. Our empirical experiment shows that the model gives a good short-term forecasting.
基金supported by the National Natural Science Foundation of China(Nos.11871009,12271055)the Foundation of LCP and the Foundation of CAEP(CX20210044).
文摘Based on the idea of serendipity element,we construct and analyze the first quadratic serendipity finite volume element method for arbitrary convex polygonalmeshes in this article.The explicit construction of quadratic serendipity element shape function is introduced from the linear generalized barycentric coordinates,and the quadratic serendipity element function space based on Wachspress coordinate is selected as the trial function space.Moreover,we construct a family of unified dual partitions for arbitrary convex polygonal meshes,which is crucial to finite volume element scheme,and propose a quadratic serendipity polygonal finite volume element method with fewer degrees of freedom.Finally,under certain geometric assumption conditions,the optimal H1 error estimate for the quadratic serendipity polygonal finite volume element scheme is obtained,and verified by numerical experiments.
基金supported by the Major Science and Technology Program for Water Pollution Control and Treatment(No.2012ZX07212001)the National Natural Science Foundation of China(No.31570505)the State Key Laboratory of Urban Water Resource and Environment,Harbin Institute of Technology(No.2014TS05)
文摘Atrazine, a widely used herbicide, is increasing the agricultural production effectively, while also causing great environmental concern. Efficient atrazine-degrading bacterium is necessary to removal atrazine rapidly to keep a safe environment. In the present study, a new atrazine-degrading strain ZXY-1, identified as Pseudomonas, was isolated. This new isolated strain has a strong ability to biodegrade atrazine with a high efficiency of 9.09 mg/L/hr.Temperature, p H, inoculum size and initial atrazine concentration were examined to further optimize the degradation of atrazine, and the synthetic effect of these factors were investigated by the response surface methodology. With a high quadratic polynomial mathematical model(R^2= 0.9821) being obtained, the highest biodegradation efficiency of 19.03 mg/L/hr was reached compared to previous reports under the optimal conditions(30.71°C, pH 7.14, 4.23%(V/V) inoculum size and 157.1 mg/L initial atrazine concentration).Overall, this study provided an efficient bacterium and approach that could be potentially useful for the bioremediation of wastewater containing atrazine.
基金This work is supported by the National Natural Science Foundation of China(No.11371154)the Foundation for Distinguished Young Talents in Higher Education of Guangdong(No.3XZ150603)Characteristic innovation project of Guangdong(No.2015KTSCX1).
文摘In the paper,we consider the l_(1)-regularized least square problem which has been intensively involved in the fields of signal processing,compressive sensing,linear inverse problems and statistical inference.The considered problem has been proved recently to be equivalent to a nonnegatively constrained quadratic programming(QP).In this paper,we use a recently developed active conjugate gradient method to solve the resulting QP problem.To improve the algorithm’s performance,we design a subspace exact steplength as well as a precondition technique.The performance comparisons illustrate that the proposed algorithm is competitive and even performs little better than several state-of-the-art algorithms.
文摘Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a problem of the initial boundary values for a system of 3-dimensional nonlinear parabolic partial differential equations, one being the pressure flow equation and the other is the concentration convection-dispersion equation of the salt contained. For a generic case of a 3-dimensional bounded region, a backward-difference time-stepping scheme is defined. It approximates the pressure by the standard Galerkin procedure and the concentration by a Galerkin method of charederistics, where calculus of variations, theory of prior estimates and techniques are made use of Optimal order estimates in H1 norm are derived for the errors in the approximate solution.
基金supported by the Key-Area Research and Development Program of Guangdong Province(grant no.2020B0909-19005)the National Natural Science Foundation of China(grant nos.21975056 and 22179025)+1 种基金The Major and Special Project in the Field of Intelligent Manufacturing of the Universities in Guangdong Province(grant no.2020ZDZX2067)the Natural Science Foundation of Huizhou University(grant no.HZU202004).
文摘With advantages of low costs and high energy density,Li–S batteries are considered as one of the most promising energy storage devices.However,Li_(2)S_(2) with a high dissociation energy and insulative properties is hard to convert into Li_(2)S,resulting in underutilization of sulfur capacity.Herein,Co-Mo_(2)C@C yolk–shell spheres as nanoreactors were designed to confront this challenge rationally.The Co-Mo_(2)C@C-induced Li_(2)S_(1/2) nucleation and growth in the three-dimensional process and the cathode produced more Li_(2)S after full discharge.Experimental studies and theoretical calculations reveal that the conversion barrier from Li_(2)S_(2) into Li_(2)S was lowered while the diffusion of lithium ions and electron transfer accelerated when using the Co-Mo_(2)C@C catalyst.Based on the above advantages,the Co-Mo_(2)C@C/S cathode exhibits a high reversible capacity and excellent cyclic stability,such as an initial specific capacity of 1200 mAh g^(−1) at 0.1 C with 709 mAh g^(−1) at 1.0 C after 1000 cycles with a low capacity fading rate of 0.04%per cycle.Even at high densities of 3.0 C and 5.0 C,the specific capacities are 647.6 and 557.7 mAh g^(−1) after 400 cycles,respectively.Impressively,it also shows ca.770 and 900 mAh g^(−1) at 0.2 C after 50 cycles with high sulfur loadings of 4.2 and 5.1 mg cm−2,respectively.The present work may provide new insights into the design of nanoreactors to promote Li_(2)S_(1/2) growth in a three-dimensional process and accelerate conversion from solid Li_(2)S_(2) to solid Li_(2)S in high performance Li–S batteries.