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
This study utilizes a time-precedence network technique to construct two models of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）, individually including the progre...This study utilizes a time-precedence network technique to construct two models of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）, individually including the progress payment （PP） and the payment at an equal time interval （ETI）. The objective of each model is to maximize the net present value （NPV） for all cash flows in the project, subject to the related operational constraints. The models are characterized as NP-hard. A heuristic algorithm, coupled with two upper bound solutions, is proposed to efficiently solve the models and evaluate the heuristic algorithm performance which was not performed in past studies. The results show that the performance of proposed models and heuristic algorithm is good.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
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.
文摘This study utilizes a time-precedence network technique to construct two models of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）, individually including the progress payment （PP） and the payment at an equal time interval （ETI）. The objective of each model is to maximize the net present value （NPV） for all cash flows in the project, subject to the related operational constraints. The models are characterized as NP-hard. A heuristic algorithm, coupled with two upper bound solutions, is proposed to efficiently solve the models and evaluate the heuristic algorithm performance which was not performed in past studies. The results show that the performance of proposed models and heuristic algorithm is good.
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.
