The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some f...The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function was proposed. The definition of the original filled function and assumptions of the objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30展开更多
In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continu...In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
We report results from ab-initio, self-consistent density functional theory (DFT) calculations of electronic, transport and bulk properties of rock salt magnesium sulfide (MgS). In the absence of experimental data on ...We report results from ab-initio, self-consistent density functional theory (DFT) calculations of electronic, transport and bulk properties of rock salt magnesium sulfide (MgS). In the absence of experimental data on these properties, except for the bulk modulus, these results are predictions. Our calculations utilized the Ceperley and Alder local density approximation (LDA) potential and the linear combination of Gaussian orbitals (LCGO). The key difference between our computations and other previous ab-initio DFT ones stems from our use of successively larger basis sets, in consecutive, self-consistent calculations, to attain the ground state of the material. We predicted an indirect (Γ-X) band gap of 3.278 eV for a room temperature lattice constant of 5.200Å. We obtained a predicted low temperature indirect (Γ-X) band gap of 3.512 eV, using the equilibrium lattice constant of 5.183Å. We found a theoretical value of 79.76 GPa for the bulk modulus;it agrees very well with the experimental finding of 78 ±3.7 GPa.展开更多
In the first of a series of papers,wewill study a discontinuous Galerkin(DG)framework for many electron quantum systems.The salient feature of this framework is the flexibility of using hybrid physics-based local orbi...In the first of a series of papers,wewill study a discontinuous Galerkin(DG)framework for many electron quantum systems.The salient feature of this framework is the flexibility of using hybrid physics-based local orbitals and accuracy-guaranteed piecewise polynomial basis in representing the Hamiltonian of the many body system.Such a flexibility is made possible by using the discontinuous Galerkin method to approximate the Hamiltonian matrix elements with proper constructions of numerical DG fluxes at the finite element interfaces.In this paper,we will apply the DG method to the density matrix minimization formulation,a popular approach in the density functional theory of many body Schrodinger equations.The density matrix minimization is to find the minima of the total energy,expressed as a functional of the density matrixρ(r,r′),approximated by the proposed enriched basis,together with two constraints of idempotency and electric neutrality.The idempotency will be handled with theMcWeeny’s purification while the neutrality is enforced by imposing the number of electrons with a penalty method.A conjugate gradient method(a Polak-Ribiere variant)is used to solve the minimization problem.Finally,the linear-scaling algorithm and the advantage of using the local orbital enriched finite element basis in the DG approximations are verified by studying examples of one dimensional lattice model systems.展开更多
文摘The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function was proposed. The definition of the original filled function and assumptions of the objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30
文摘In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
文摘We report results from ab-initio, self-consistent density functional theory (DFT) calculations of electronic, transport and bulk properties of rock salt magnesium sulfide (MgS). In the absence of experimental data on these properties, except for the bulk modulus, these results are predictions. Our calculations utilized the Ceperley and Alder local density approximation (LDA) potential and the linear combination of Gaussian orbitals (LCGO). The key difference between our computations and other previous ab-initio DFT ones stems from our use of successively larger basis sets, in consecutive, self-consistent calculations, to attain the ground state of the material. We predicted an indirect (Γ-X) band gap of 3.278 eV for a room temperature lattice constant of 5.200Å. We obtained a predicted low temperature indirect (Γ-X) band gap of 3.512 eV, using the equilibrium lattice constant of 5.183Å. We found a theoretical value of 79.76 GPa for the bulk modulus;it agrees very well with the experimental finding of 78 ±3.7 GPa.
基金support of U.S.Army Research Office(grant number W911NF-11-1-0364)support of NSFC(grant number 11011130029)and of SRF for ROCS,SEM.
文摘In the first of a series of papers,wewill study a discontinuous Galerkin(DG)framework for many electron quantum systems.The salient feature of this framework is the flexibility of using hybrid physics-based local orbitals and accuracy-guaranteed piecewise polynomial basis in representing the Hamiltonian of the many body system.Such a flexibility is made possible by using the discontinuous Galerkin method to approximate the Hamiltonian matrix elements with proper constructions of numerical DG fluxes at the finite element interfaces.In this paper,we will apply the DG method to the density matrix minimization formulation,a popular approach in the density functional theory of many body Schrodinger equations.The density matrix minimization is to find the minima of the total energy,expressed as a functional of the density matrixρ(r,r′),approximated by the proposed enriched basis,together with two constraints of idempotency and electric neutrality.The idempotency will be handled with theMcWeeny’s purification while the neutrality is enforced by imposing the number of electrons with a penalty method.A conjugate gradient method(a Polak-Ribiere variant)is used to solve the minimization problem.Finally,the linear-scaling algorithm and the advantage of using the local orbital enriched finite element basis in the DG approximations are verified by studying examples of one dimensional lattice model systems.
基金The National Natural Science Foundation of China (10571137 and 10571116)the Great Natural Science Foundation of Henan University of Science and Technology (2005ZD006)
