This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The en...This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero. This new algorithm has more flexibility for the acceptance of the trial step and requires less computational costs compared with traditional filter algorithm. The global and local convergence of the proposed algorithm are given under some reasonable conditions. The numerical experiments are reported to show the effectiveness of the dwindling filter algorithm.展开更多
The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization.The feasibility restoration phase,which is always used in the traditional filter m...The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization.The feasibility restoration phase,which is always used in the traditional filter method,is not needed.Under mild conditions,global convergence and local superlinear convergence rates are obtained.Numerical results demonstrate that the new algorithm is effective.展开更多
dwindle(动词)该词的意思是“收缩；缩小；逐渐减少，逐渐削弱”。英语的释义是to decrease or shrink；to become less。没有人相信笨手笨脚的人竟然敢去偷窃，然而，在《亨利王四世上篇》(The First Part of King Henry IV)中，Falst...dwindle(动词)该词的意思是“收缩；缩小；逐渐减少，逐渐削弱”。英语的释义是to decrease or shrink；to become less。没有人相信笨手笨脚的人竟然敢去偷窃，然而，在《亨利王四世上篇》(The First Part of King Henry IV)中，Falstaff爵士竟然这么做了。展开更多
Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new...Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11201304,11371253the Innovation Program of Shanghai Municipal Education Commission under Grant No.12YZ174Group of Accounting and Governance Disciplines(10kq03)
文摘This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero. This new algorithm has more flexibility for the acceptance of the trial step and requires less computational costs compared with traditional filter algorithm. The global and local convergence of the proposed algorithm are given under some reasonable conditions. The numerical experiments are reported to show the effectiveness of the dwindling filter algorithm.
基金supported by the National Natural Science Foundation of China(Nos.11201304,11371253)the Innovation Program of Shanghai Municipal Education Commission(No.12YZ174)the Group of Accounting and Governance Disciplines(No.10kq03)
文摘The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization.The feasibility restoration phase,which is always used in the traditional filter method,is not needed.Under mild conditions,global convergence and local superlinear convergence rates are obtained.Numerical results demonstrate that the new algorithm is effective.
文摘dwindle(动词)该词的意思是“收缩；缩小；逐渐减少，逐渐削弱”。英语的释义是to decrease or shrink；to become less。没有人相信笨手笨脚的人竟然敢去偷窃，然而，在《亨利王四世上篇》(The First Part of King Henry IV)中，Falstaff爵士竟然这么做了。
基金Supported by National Natural Science Foundation of China(Grant Nos.11201304 and 11371253)the Innovation Program of Shanghai Municipal Education Commission
文摘Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.
