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911.
912.
对Floyd算法的两点注记 总被引:14,自引:1,他引:13
本给Floyd算法配置了一种更便于使用的路径标记方法,还给出了在无向网络上减少Floyd算法的计算量的方法。 相似文献
913.
《泛函分析》中两个定理的教学与应用 总被引:2,自引:0,他引:2
刘迎东 《数学的实践与认识》2001,31(2):251-253
本文讨论《泛函分析》中 Schauder不动点定理和 Arzela-Ascoli定理的教学方法并把它们用于互助生态模型得到两物种共存的一个充分条件 . 相似文献
914.
De Tong Zhu 《数学学报(英文版)》2008,24(12):2081-2100
We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed. 相似文献
915.
在Mann的迭代算法基础上,运用Banach空间中的广义投影,使渐进非扩展映像每次迭代生成的序列都投影到一个闭凸的集合中.并证明了该算法的强收敛性. 相似文献
916.
基于最优化方法求解约束非线性方程组的一个突出困难是计算 得到的仅是该优化问题的稳定点或局部极小点,而非方程组的解点.由此引出的问题是如何从一个稳定点出发得到一个相对于方程组解更好的点. 该文采用投影型算法,推广了Nazareth-Qi$^{[8,9]}$ 求解无约束非线性方程组的拉格朗日全局算法(Lagrangian Global-LG)于约束方程上; 理论上证明了从优化问题的稳定点出发,投影LG方法可寻找到一个更好的点. 数值试验证明了LG方法的有效性. 相似文献
917.
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way. 相似文献
918.
Pier Luigi Papini 《TOP》2005,13(2):315-320
Many problems in continuous location theory, reduce to finding a best location, in the sense that a facility must be located
at a point minimizing the sum of distances to the points of a given finite set (median) or the largest distances to all points
(center). The setting is often assumed to be a Banach space.
To have a better understanding concerning the structure of location problems, it may occur also in rather simple cases.
In this paper we indicate two simple examples of four-point sets such that one of the two problems indicated has a solution,
while the other one has no solution. Also, we list papers containing examples previously given, dealing with this lack of
optimal solutions. 相似文献
919.
Jianxin Zhou. 《Mathematics of Computation》2005,74(251):1391-1411
The objective of this work is to develop some tools for local instability analysis of multiple critical points, which can be computationally carried out. The Morse index can be used to measure local instability of a nondegenerate saddle point. However, it is very expensive to compute numerically and is ineffective for degenerate critical points. A local (weak) linking index can also be defined to measure local instability of a (degenerate) saddle point. But it is still too difficult to compute. In this paper, a local instability index, called a local minimax index, is defined by using a local minimax method. This new instability index is known beforehand and can help in finding a saddle point numerically. Relations between the local minimax index and other local instability indices are established. Those relations also provide ways to numerically compute the Morse, local linking indices. In particular, the local minimax index can be used to define a local instability index of a saddle point relative to a reference (trivial) critical point even in a Banach space while others failed to do so.
920.
Meiyu Zhang 《Journal of Mathematical Analysis and Applications》2008,339(2):970-981
In this paper, ? convex −ψ concave mixed monotone operators are introduced and some new existence and uniqueness theorems of fixed points for mixed monotone operators with such convexity concavity are obtained. As an application, we give one example to illustrate our results. 相似文献