关键词： M-matrix algebraic Riccati equation   minimal nonnegative solution   critical case   two-phase structure-preserving doubling algorithm   M-matrix  

摘要： Among numerous iterative methods for solving the minimal nonnegative solution of an M-matrix algebraic Riccati equation, the structure-preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank-one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank-one component can be accurately recovered. We then propose an efficient hybrid method, called the two-phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two-phase SDA saves those SDA iterative steps that previously have to have for the rank-one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two-phase SDA. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： smooth surface   convex programming problem   projection onto a nonconvex set   necessary conditions for a local minimum   convergence of an algorithm  

摘要： A numerical algorithm for minimizing a convex function on a smooth surface is proposed. The algorithm is based on reducing the original problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.

关键词： Molecular sieve carbon membranes   Gas permeation   Mathematical modeling   Transport properties   Genetic algorithm  

摘要： Permeation of N-2, CH4, O-2 and CO2 molecules through a carbon molecular sieve (CMS) was studied over a wide range of pressures using the transport mechanism For proper utilization of carbon molecular sieve membrane in gas separation processes, prediction of behavior and recognition of proper gas transport mechanism as well as finding effective permeation parameters are necessary. A mathematical model of the gas transfer through a CMS membrane was developed using genetic algorithm (GA). Numerous types of mechanisms have been proposed so far for gas transport through capillaries, namely: Knudsen, slip and viscous flow. Moreover, surface flow usually occurs in parallel with other transport mechanisms such as Knudsen or viscous flow. The experimental data of gas permeation in CMS membranes and an appropriate genetic algorithm-based optimization method were used to establish the transport parameters. A GA, an optimization procedure based on the theory of evolution, was compared with non-linear regression for the ability of these two algorithms to fit the coefficients of Poultry growth models. It was found that GA approach could be more capable to define the parameters of permeation equation than non-linear regression. The model in most cases showed a good agreement between the predicted and measured values of the permeability.

关键词： local ventilation suction port   dust particles   limiting trajectories   ventilation   method of discrete vortices  

摘要： A mathematical model and computer program for use in calculating the separation region at the inlet to a funnel situated above an impermeable plane are developed by means of stationary discrete vortex rings. The basic computational relationships and algorithms for calculating the characteristic regions of detached flow, the limiting trajectories of dust particles, and the ventilation region are presented.

关键词： Multitrip cumulative capacitated   Single-vehicle routing problem   Disaster logistics   Resource constrained shortest path problem  

摘要： This paper addresses the multitrip Cumulative Capacitated Single-Vehicle Routing Problem (mt-CCSVRP). In this problem inspired by disaster logistics, a single vehicle can perform successive trips to serve a set of affected sites and minimize an emergency criterion, the sum of arrival times. Two mixed integer linear programs, a flow-based model and a set partitioning model, are proposed for small instances with 20 sites. An exact algorithm for larger cases transforms the mt-CCSVRP into a resource-constrained shortest path problem where each node corresponds to one trip and the sites to visit become resources. The resulting problem can be solved via an adaptation of Bellman-Ford algorithm to a directed acyclic graph with resource constraints and a cumulative objective function. Seven dominance rules, two upper bounds and five lower bounds speed up the procedure. Computational results on instances derived from classical benchmark problems for the capacitated VRP indicate that the exact algorithm outperforms a commercial MIP solver on small instances and can solve cases with 40 sites to optimality. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： 定位   数学模型   粒子滤波   静止目标  

摘要： 粒子滤波算法在目标定位中主要用于目标跟踪,对静止目标定位的应用研究鲜有报道,尤其是针对具体的无线电移动监测车,已知数据只有车的位置坐标和目标示向度情况,数学模型的建立还没有文献可供参考。在熟悉粒子滤波机理的基础上,参考粒子滤波在目标跟踪时建立数学模型的方法,结合无线电移动监测车对静止目标定位的实际需要,建立粒子滤波算法在静止目标定位时的数学模型,模型中融合分类和择优的措施以提高定位精度。最后在LabVIEW平台下对所建立的模型进行仿真实验,结果表明所建立的模型准确可行。

关键词： 遗传算法   最小二乘法   非线性超定方程组  

摘要： 遗传算法的基本思想是基于模仿生物界一种的遗传过程,把问题的用基因代表参数,把问题的用染色体代表二进制解从而得到一个群体,主要由三个基本操作构成:选择、交叉、变异。最小二乘法则为已知一组实验数据(x_i,y_i),i=0.1,…,m,求自变量X与因变量V之间的函数关系y=f(x),只要求在给定点的误差δ=f(x_i)y_i,残差的平方和最小,∑_(i=0)~mδ_i^2=∑_(i=0)~m(y_i-f(x_i))~2=min。本文基于2015年全国大学生数学建模获奖作品提出了一种改进遗传算法,结合最小二乘法,利用IVlkTLAB,JAVA软件对太阳影子定位问题进行数学建模分析。