一类m-点边值问题的正解

研究一类二阶m-点边值问题u″ f(t,u,u)′=0,00,i=1,…,m-2,ζi满足0=ζ0<ζ1<ζ2<…<ζm-2<ζm-1=1和i∑=1aiζi<1。应用推广的Krasnosel-skii′s不动点定理,给出了上述边值问题至少存在一个正解的充分条件。     

一种非均匀噪声下的DOA估计算法

通用协方差差分算法用来实现对空间非均匀噪声环境下相干信号的波达方向(DOA)估计,该算法可以完全消除空间非均匀噪声,且适用于低信噪比环境,但该算法的DOA估计结果存在伪峰。针对这一问题,提出了一种改进的算法。改进算法通过对通用协方差差分(GCD)算法的信号协方差矩阵进行变换,再用特征分解的方法得到信号的DOA估计值。改进的算法可以完全消除伪峰,理论分析和仿真实验验证了改进算法的有效性。     

基于MIDAS的大跨度斜拉桥行波效应分析

针对宜巴段三塔四跨斜拉桥工程实例,结合MIDAS软件,进行动态时程分析,对比研究了行波效应对桥塔、桥墩各控制点的位移、剪力以及轴力的纵向地震反应的影响。通过施加-EL-Centro纵向地震波作用,模拟出斜拉桥控制点的位移、内力地震反应最大值,得出结论：对于多塔斜拉桥,行波效应对各桥塔塔底、各桥塔塔顶内力、位移响应的影响不同。     

用于目标跟踪的自适应广义调频波形设计算法

提出了一种用于雷达目标跟踪的自适应广义调频波形设计算法。该算法根据跟踪器的动态需求,以广义调频信号为样板波形自适应设计下一时刻的发射波形,其目的是使预测的目标跟踪均方误差最小化,并假定高信噪比条件,且目标跟踪运动模型和观测模型均为线性。利用与某一波形相对应的克拉美-罗下限(CRLB)以及卡尔曼滤波器,通过最小化预测的跟踪均方误差来实现广义调频波形的自适应设计。仿真结果表明:在信噪比相同的情况下,与使用固定参数、自适应参数的线性调频波形设计算法相比,所提出的算法能够获得更低的目标跟踪均方误差。     

混合均衡问题和不动点问题的公共元的迭代算法

在Hilbert空间中,利用超梯度算法,用以逼近混合均衡问题的解集与半压缩映像不动点集的公共元,并且证明了该算法的收敛性。使用新的分析技巧证明了一个强收敛定理。     

上、下半连续性关系及其在经济上的应用

上、下半连续性在数学中的重要性不言而喻,在微观经济分析中也有着广泛应用,特别是静态优化问题。分别在单值映射、集值映射中探讨了上半连续性和下半连续性的关系。先证明了单值映射上、下半连续性等价的结论(定理1),并利用引理1对常见函数的上、下半连续性进行了探讨以进一步说明定理1;然后通过举反例进行论证,得出了集值映射中上、下半连续性不等价的结论(定理2);最后例举了上、下半连续性在数理经济上的应用,具有创新价值。通过对数理经济学中参数约束最优化问题的最大值定理(引理2)条件和结论所做的两点注记,并附以具体实例予以解释,说明了单、集值映射中上、下半连续性的关系,以及在数理经济上的重要应用。     

A generalized assignment model for dynamic supply chain capacity planning

We consider a generalization of the well‐known generalized assignment problem (GAP) over discrete time periods encompassed within a finite planning horizon. The resulting model, MultiGAP, addresses the assignment of tasks to agents within each time period, with the attendant single‐period assignment costs and agent‐capacity constraint requirements, in conjunction with transition costs arising between any two consecutive periods in which a task is reassigned to a different agent. As is the case for its single‐period antecedent, MultiGAP offers a robust tool for modeling a wide range of capacity planning problems occurring within supply chain management. We provide two formulations for MultiGAP and establish that the second (alternative) formulation provides a tighter bound. We define a Lagrangian relaxation‐based heuristic as well as a branch‐and‐bound algorithm for MultiGAP. Computational experience with the heuristic and branch‐and‐bound algorithm on over 2500 test problems is reported. The Lagrangian heuristic consistently generates high‐quality and in many cases near‐optimal solutions. The branch‐and‐bound algorithm is also seen to constitute an effective means for solving to optimality MultiGAP problems of reasonable size. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

A mathematical programming approach for improving the robustness of least sum of absolute deviations regression

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least‐sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

货郎担问题新算法

将指派问题的匈牙利解法用于货郎担问题,通过恰当地添加大正数构造效率矩阵,得到了计算货郎担问题较快的算法。文中给出的2个例子具体地说明了算法实施过程,该算法具有一定的实用性。     

网络化作战C2组织结构的一种分析设计方法

网络化作战条件下,传统的层次型C2组织限制了组织成员之间的信息交互,难以适应复杂多变的作战环境,影响了系统整体作战效能的发挥。通过分解单个组织节点智能体(Agent)的行为过程,结合网络化作战的概念,在引入信息流、指控流因素情况下,研究在网络化作战中C2组织结构网络,并在分析组织网络探测信息/指控命令的传输和处理的基础上,提出了一种C2组织结构设计方法。该方法充分考虑了网络化作战探测信息共享以及指控命令协同,并将网络化作战C2组织的最优设计问题转化为C2组织网络中探测信息和指控命令的最小费用最大流问题。