基于凸优化理论的三维微分对策制导规律求解

针对三维微分对策制导律(DGL)求解问题,引入凸优化理论,将DGL求解归结到Hamilton系统的求解,设计了DGL求解算法,通过对代价函数梯度特征的凸分析,推导出对策系统鞍点存在的充要条件和求解方法,解决了以往通过对微分对策模型简化求解导致的模型不能客观反映作战过程的问题.     

基于凸-改进遗传算法的圆阵列方向图联合优化

针对圆形阵列方向图具有较高旁瓣的问题,提出一种新的基于凸优化和改进遗传算法的优化方法。该方法首先采用遗传算法将阵元位置和阵元权值作为优化变量,以最小化波束方向图峰值旁瓣为目标函数进行联合优化,既增加了变量的自由度,又符合理论意义上的全局寻优;同时,为了避免算法的早熟收敛,对基本遗传算法进行了必要的改进。然后采用凸优化方法对阵元权值进行二次优化可进一步降低旁瓣电平,与传统方法相比能够明显提高优化效果的稳定性。仿真数据证实了该方法的有效性和正确性。     

Concave envelopes of monomial functions over rectangles

The construction of convex and concave envelopes of real‐valued functions has been of interest in mathematical programming for over 3 decades. Much of this interest stems from the fact that convex and concave envelopes can play important roles in algorithms for solving various discrete and continuous global optimization problems. In this article, we use a simplicial subdivision tool to present and validate the formula for the concave envelope of a monomial function over a rectangle. Potential algorithmic applications of this formula are briefly indicated. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Stein–Chen approximation and error bounds for order fill rates in assemble‐to‐order systems

Assemble‐to‐order (ATO) is an important operational strategy for manufacturing firms to achieve quick response to customer orders while keeping low finished good inventories. This strategy has been successfully used not only by manufacturers (e.g., Dell, IBM) but also by retailers (e.g., Amazon.com). The evaluation of order‐based performance is known to be an important but difficult task, and the existing literature has been mainly focused on stochastic comparison to obtain performance bounds. In this article, we develop an extremely simple Stein–Chen approximation as well as its error‐bound for order‐based fill rate for a multiproduct multicomponent ATO system with random leadtimes to replenish components. This approximation gives an expression for order‐based fill rate in terms of component‐based fill rates. The approximation has the property that the higher the component replenishment leadtime variability, the smaller the error bound. The result allows an operations manager to analyze the improvement in order‐based fill rates when the base‐stock level for any component changes. Numerical studies demonstrate that the approximation performs well, especially when the demand processes of different components are highly correlated; when the components have high base‐stock levels; or when the component replenishment leadtimes have high variability. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks

A simultaneous non‐zero‐sum game is modeled to extend the classical network interdiction problem. In this model, an interdictor (e.g., an enforcement agent) decides how much of an inspection resource to spend along each arc in the network to capture a smuggler. The smuggler (randomly) selects a commodity to smuggle—a source and destination pair of nodes, and also a corresponding path for traveling between the given pair of nodes. This model is motivated by a terrorist organization that can mobilize its human, financial, or weapon resources to carry out an attack at one of several potential target destinations. The probability of evading each of the network arcs nonlinearly decreases in the amount of resource that the interdictor spends on its inspection. We show that under reasonable assumptions with respect to the evasion probability functions, (approximate) Nash equilibria of this game can be determined in polynomial time; depending on whether the evasion functions are exponential or general logarithmically‐convex functions, exact Nash equilibria or approximate Nash equilibria, respectively, are computed. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 139–153, 2017     

多边形障碍环境中避障路径的遗传算法

研究了平面障碍环境中避障的遗传算法,重点介绍了障碍环境的模型构造和用遗传算法求解该模型的方法设计.采用了与已有遗传算法不同的染色体编码方式和不同的遗传算子设计,在初始群体产生时尽量避免了引入无效基因,提高了染色体进化的效率,使得该算法具有很好的寻优能力,实验结果也表明了该算法的有效性.     

固体推进剂药柱结构分析的非概率凸集合理论模型

为了研究不确定性能参数对固体推进剂药柱结构分析的影响 ,将非概率凸集合理论模型和粘弹性有限元相结合 ,以增量法处理遗传积分 ,利用摄动法预测其响应量区间 ,发展了一种适合药柱特点的不确定性方法。将其和随机结构分析进行对比 ,表明两种方法之间有一定的联系。     

凸集支撑函数的性质及其应用

本文讨论一个凸集C 的支撑函数的几个有用性质,并把这些性质应用于对函数次微分的研究,得到有关函数次微分的几个有趣结果。     

关于强增生算子的非线性方程迭代解

利用两种迭代法(Mann和Ishikawa)给出了非线性方程Tx=f解的逼近。     

利用詹森不等式推广几个数学问题

詹森（Jensen）不等式是解决不等式问题的一个重要方法，也是发现数学问题的重要手段。运用詹森不等式的关键是通过观察所给代数式的函数特征，构造一个凹或凸的函数，以利解题。