In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices ou...In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.展开更多
This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the gl...This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.展开更多
In this paper, the Crank-Nicolson/Newton scheme for solving numerically second- order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the...In this paper, the Crank-Nicolson/Newton scheme for solving numerically second- order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nieolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank- Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the efficient performance of the proposed scheme.展开更多
The volatile wind power generation brings a full spectrum of problems to power system operation and management, ranging from transient system frequency fluctuation to steady state supply and demand balancing issue. In...The volatile wind power generation brings a full spectrum of problems to power system operation and management, ranging from transient system frequency fluctuation to steady state supply and demand balancing issue. In this paper, a novel wind integrated power system day-ahead economic dispatch model, with the consideration of generation and reserve cost is modelled and investigated. The proposed problem is first formulated as a chance constrained stochastic nonlinear programming(CCSNLP), and then transformed into a deterministic nonlinear programming(NLP). To tackle this NLP problem, a three-stage framework consists of particle swarm optimization(PSO), sequential quadratic programming(SQP) and Monte Carlo simulation(MCS) is proposed. The PSO is employed to heuristically search the line power flow limits, which are used by the SQP as constraints to solve the NLP problem. Then the solution from SQP is verified on benchmark system by using MCS. Finally, the verified results are feedback to the PSO as fitness value to update the particles. Simulation study on IEEE30-bus system with wind power penetration is carried out, and the results demonstrate that the proposed dispatch model could be effectively solved by the proposed three-stage approach.展开更多
In this paper, a new limited memory quasi-Newton method is proposed and developed for solving large-scale linearly equality-constrained nonlinear programming problems. In every iteration, a linear equation subproblem ...In this paper, a new limited memory quasi-Newton method is proposed and developed for solving large-scale linearly equality-constrained nonlinear programming problems. In every iteration, a linear equation subproblem is solved by using the scaled conjugate gradient method. A truncated solution of the subproblem is determined so that computation is decreased. The technique of limited memory is used to update the approximated inverse Hessian matrix of the Lagrangian function. Hence, the new method is able to handle large dense problems. The convergence of the method is analyzed and numerical results are reported.展开更多
基金The research was supported by the State Education Grant for Retumed Scholars
文摘In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.
文摘This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.
基金in part supported by the Distinguished Young Scholars Fund of Xinjiang Province(2013711010)NCET-13-0988the NSF of China(11271313,11271298,61163027,and 11362021)
文摘In this paper, the Crank-Nicolson/Newton scheme for solving numerically second- order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nieolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank- Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the efficient performance of the proposed scheme.
基金supported in part by the National Science Foundation(ECCS1053717,CNS 1117314)the National Science Foundation of China(51529701,51277135)
文摘The volatile wind power generation brings a full spectrum of problems to power system operation and management, ranging from transient system frequency fluctuation to steady state supply and demand balancing issue. In this paper, a novel wind integrated power system day-ahead economic dispatch model, with the consideration of generation and reserve cost is modelled and investigated. The proposed problem is first formulated as a chance constrained stochastic nonlinear programming(CCSNLP), and then transformed into a deterministic nonlinear programming(NLP). To tackle this NLP problem, a three-stage framework consists of particle swarm optimization(PSO), sequential quadratic programming(SQP) and Monte Carlo simulation(MCS) is proposed. The PSO is employed to heuristically search the line power flow limits, which are used by the SQP as constraints to solve the NLP problem. Then the solution from SQP is verified on benchmark system by using MCS. Finally, the verified results are feedback to the PSO as fitness value to update the particles. Simulation study on IEEE30-bus system with wind power penetration is carried out, and the results demonstrate that the proposed dispatch model could be effectively solved by the proposed three-stage approach.
基金This research is supported by the National Natural Science Foundation of China, LSEC of CAS in Beijingand Natural Science Foun
文摘In this paper, a new limited memory quasi-Newton method is proposed and developed for solving large-scale linearly equality-constrained nonlinear programming problems. In every iteration, a linear equation subproblem is solved by using the scaled conjugate gradient method. A truncated solution of the subproblem is determined so that computation is decreased. The technique of limited memory is used to update the approximated inverse Hessian matrix of the Lagrangian function. Hence, the new method is able to handle large dense problems. The convergence of the method is analyzed and numerical results are reported.
基金Supported by the National Science Foundation of China(No.10671126)Shanghai Municipal Committee of Science and Technology(No.10550500800)Shanghai Leading Discipline Project(No.S30501)
