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。     

Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Iterative coloring extension of a maximum clique

In this paper we present an improved branch and bound algorithm for the vertex coloring problem. The idea is to try to extend the coloring of a maximum clique to its adjacent vertices. If this succeeds, its successive neighbors are considered; in case of failure (i.e., in the case the initial colors are not sufficient), working on the subgraph induced by the maximum clique and its neighborhood, the lower bound is improved by seeking for an optimal coloring of this subgraph by branch and bound. The process is repeated iteratively until the whole graph is examined. The iterative scheme exploits a further lower bound obtained by integrating a simple algorithm into the maximum clique search, and a new method to compute upper bounds on subgraphs. Furthermore, a new branching rule and a method for the selection of the initial maximum clique are presented. Extensive computational results and comparisons with existing exact coloring algorithms on random graphs and benchmarks are given. © 2001 John Wiley & Sons, Inc. Naval Research Logistic 48: 518–550, 2001     

指数寿命产品可靠性增长试验的Bayes分析

针对指数寿命产品的定时、定数截尾试验方案,推广了Mazzuchi-Soyer模型的应用范围。首先引入模型假设,以狄氏分布作为先验分布,综合利用产品研制的历史信息和专家信息,结合产品研制各阶段试验数据,给出了各阶段可靠性的联合后验分布。然后利用Gibbs抽样算法解决后验推断计算问题,得到各阶段产品可靠性的Bayes点估计和区间估计。最后给出产品可靠性增长分析实例,表明了模型的优越性。     

Minimizing makespan in a multimode multiprocessor shop scheduling problem

We study the problem of multimode scheduling tasks on dedicated processors, with the objective of minimizing the maximum completion time. Each task can be undertaken in one among a set of predefined alternative modes, where each mode specifies a required set of dedicated processors and a processing time. At any time each processor can be used by a single task at most. General precedence constraints exist among tasks, and task preemption is not allowed. The problem consists of assigning a mode and a starting time to each task, respecting processor and precedence constraints, to minimize the time required to complete all tasks. The problem is NP-hard in several particular cases. In previous works, we studied algorithms in which a solution was obtained by means of an iterative procedure that combines mode assignment and sequencing phases separately. In this paper, we present some new heuristics where the decision on the mode assignment is taken on the basis of a partial schedule. Then, for each task, the mode selection and the starting time are chosen simultaneously considering the current processor usage. Different lower bounds are derived from a mathematical formulation of the problem and from a graph representation of a particular relaxed version of the problem. Heuristic solutions and lower bounds are evaluated on randomly generated test problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 893–911, 1999     

Scheduling deteriorating jobs to minimize makespan

We consider a single-machine problem of scheduling n independent jobs to minimize makespan, in which the processing time of job J_j grows by w_j with each time unit its start is delayed beyond a given common critical date d. This processing time is p_j if J_j starts by d. We show that this problem is NP-hard, give a pseudopolynomial algorithm that runs in time and O(nd) space, and develop a branch-and-bound algorithm that solves instances with up to 100 jobs in a reasonable amount of time. We also introduce the case of bounded deterioration, where the processing time of a job grows no further if the job starts after a common maximum deterioration date D > d. For this case, we give two pseudopolynomial time algorithms: one runs in O(n²d(D − d) time and O(nd(D − d)) space, the other runs in p_j)²) time and p_j) space. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 511–523, 1998     

初始误差和制导工具误差估计的非线性方法

准确估计初始误差和制导工具误差是机动发射飞行器精度鉴定必须解决的重要问题之一,提出了一种基于非线性模型的误差估计新方法。给出了平台初始失准角向定向误差的转换方法,采用不动点迭代法实现真实视加速度的精确计算,将真实发射系的轨道参数表示为初始误差和工具误差的非线性函数,结合外测数据建立了同时估计初始误差、工具误差、外测系统误差、遥外测时间零点偏差的非线性模型,避免了初始误差的线性化近似。给出了Bayes极大后验估计方法,利用非线性模型和先验信息获得误差的最优估计,证明了估计方法的收敛性。仿真结果表明,所提方法提高了初始误差和工具误差的估计精度,并实现了测量数据的自校准。     

集群通信在消防通信调度指挥系统中的应用

无线通信网是消防部队在执行灭火抢险救援任务时，确保完成信息传达、灭火抢险救援指挥、协同作战等任务的关键。为了更好的开发集群通信的功能，介绍了集群通信的概念、组网方式，并探讨了通信区域扩展的方法。     

When are observed failures more informative than observed survivals?

A framework involving independent competing risks permits observing failures due to a specific cause and failures due to a competing cause, which constitute survival times from the cause of primary interest. Is observing more failures more informative than observing survivals? Intuitively, due to the definitiveness of failures, the answer seems to be the former. However, it has been shown before that this intuition holds when estimating the mean but not the failure rate of the exponential model with a gamma prior distribution for the failure rate. In this article, we address this question at a more general level. We show that for a certain class of distributions failures can be more informative than survivals for prediction of life length and vice versa for some others. We also show that for a large class of lifetime models, failure is less informative than survival for estimating the proportional hazards parameter with gamma, Jeffreys, and uniform priors. We further show that, for this class of lifetime models, on average, failure is more informative than survival for parameter estimation and for prediction. These results imply that the inferential purpose and properties of the lifetime distribution are germane for conducting life tests. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

基于拉盖尔模型的超声信号渡越时间测量性能分析

传统窄带模型仅能通过数值计算统计出超声信号渡越时间的测量性能。针对这一问题,提出基于拉盖尔模型计算理论克拉下限的方法。研究了拉盖尔函数及其时间导数的性质,得到时间导数内积矩阵,并将其应用到费舍尔矩阵中,能够快速精确计算克拉下限。对混合指数模型仿真表明,在高斯白噪声背景下,渡越时间方差与理论克拉下限具有良好的一致性;受窄带噪声和反射等因素影响,实测数据的渡越时间方差与理论克拉下限存在较大偏差。