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1.
杨亚光 《中国科学A辑》1993,36(12):1326-1331
本文利用一个新的鲁棒性指标,给出了一个全局收敛的用状态反馈配置鲁棒极点的算法,并证明了收敛点至少是局部最优解。  相似文献   

2.
全局收敛性是最优化算法应具备的一个基本性质,研究各种最优化算法的全局收敛性是非线性规划的一个重要理论问题.Zangwill 借助点到集映象来构成抽象算法这一研究途径,分析和综合了各种具体最优化算法的收敛特征,并且利用闭映象的概念提出了抽象算法的收敛条件,而后这方面的工作得到了广泛重视而有了很大的发展.Polak,Meyer,Huard,Denel,Yue 等人,都发展了 Zangwill 的研究工作.他们分别提出了多种抽象算法模型,并且研究了它们的收敛性.这些理论结果对具体算法的研究中有了重要和广泛的应用.  相似文献   

3.
研究了一类带Neumann边界条件的n维糖酵解模型.首先,以扩散系数d1为分歧参数,运用局部分歧理论分析了该模型非常数稳态解的局部结构.其次,利用全局分歧理论和LeraySchauder度理论讨论了非常数稳态解的全局存在性.最后,借助数值模拟证实了所得结论.分析结果表明n维糖酵解模型的空间模式可以生成.  相似文献   

4.
郭连红  汪娟 《数学进展》2022,(2):322-334
本文证明了无界区域上三维趋化模型初边值问题全局小强解的存在性.此外还研究了系统在半空间上的收敛性,证明了在H~1中,强解以(1+t)-3/4速率收敛到其相应的稳态解.  相似文献   

5.
董丽  王洪芹  潘虹 《数学杂志》2015,35(6):1453-1460
本文研究了二阶锥规划问题.利用新的最小值函数的光滑函数,给出一个求解二阶锥规划的光滑牛顿算法.算法可以从任意点出发,在每一步迭代只需求解一个线性方程组并进行一次线性搜索.在不需要满足严格互补假设条件下,证明了算法是全局收敛和局部二阶收敛的.数值试验表明算法是有效的.  相似文献   

6.
该文研究一个具有多重严重故障和非严重故障和修复功能的系统的可靠性问题. 在泛函分析理论的框架下,将系统方程组写成一个 Banach 空间中的抽象初值问题,利用算子半群方法,研究了该系统的适定性、稳态解的存在性以及稳定性.表明: 在系统模型的假定下,所研究的系统是适定的,存在非负动态解和稳态解, 特别在范数意义下动态解收敛到稳态解.从而由系统稳态解得到的系统指标是可靠的.  相似文献   

7.
董丽  周金川 《数学杂志》2015,35(1):173-179
本文研究了无约束优化问题.利用当前和前面迭代点的信息以及曲线搜索技巧产生新的迭代点,得到了一个新的求解无约束优化问题的下降方法.在较弱条件下证明了算法具有全局收敛性.当目标函数为一致凸函数时,证明了算法具有线性收敛速率.初步的数值试验表明算法是有效的.  相似文献   

8.
本文研究具有变系数和时间延迟的随机SIV流行病模型.首先证明模型存在唯一全局正解,然后利用半鞅收敛定理给出了疾病几乎处处灭绝的充分条件.  相似文献   

9.
赵艳  赵伟峰  廖伍代 《数学杂志》2014,34(2):287-294
本文研究了大规模线性方程问题的扰动Hopfield神经网络,并给出了网络收敛的判别准则.在一定条件下,网络的稳态误差一致有界或者收敛于0,网络具有较好的鲁棒性.最后数值仿真验证了方法的有效性.  相似文献   

10.
赵艳  赵伟峰  廖伍代 《数学杂志》2014,34(2):287-294
本文研究了大规模线性方程问题的扰动Hopfield神经网络, 并给出了网络收敛的判别准则. 在一定条件下, 网络的稳态误差一致有界或者收敛于0, 网络具有较好的鲁棒性. 最后数值仿真验证了方法的有效性.  相似文献   

11.
In this paper we focus on a class of polling systems encountered while modeling the ferry based wireless local area network (FWLAN). A moving ferry, while walking in a predetermined cyclic path, communicates with the static nodes (or users) of the network via a wireless link. The ferry is assumed to stop and communicate with a node that has a packet to send or to receive, when it is closest to that node. The location distribution of the node to which or from which a packet arrives is assumed to have a support of positive Lebesgue measure. These features imply that polling models with finite number of queues cannot be used to model the system. We study in this paper the continuous polling systems with service disciplines that model the use of the FWLAN (and that are more complex than the classical exhaustive or gated services). Our approach is based on discretization of the continuous polling model. We propose a special way of discretizing the continuous system such that: (1)?the known Pseudo conservation laws can be applied to obtain the stationary expected workload of the discrete systems; (2)?the limit, of these ??discretized' expected workloads, equals the stationary expected workload of the continuous system. Our results rely heavily on fixed point analysis of infinite dimensional operators.  相似文献   

12.
We present a unifying model based on retraction for several restart fixed point algorithms. The model embraces the interpretation of the algorithms in terms of stationary point problem by van der Laan and Talman and fully explains the 2-ray method.  相似文献   

13.
In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.  相似文献   

14.
Miyazawa  Masakiyo  Takada  Hiroyuki 《Queueing Systems》2001,37(1-3):199-232
This paper focuses on product form and related tractable stationary distributions in a general class of stochastic networks with finite numbers of nodes such that their network states are changed through signal transfers as well as internal transitions. Signals may be customers in traditional queueing applications, but we do not make any restriction on their effects at departing as well as arriving nodes. They may also instantaneously move around among different nodes. Furthermore, signal routing may depend on the whole network state. For analytical simplicity, we assume that the state space is countable. For such a network, we propose an abstract model, called a stochastic transfer network, and consider the stationary distribution of the network state. We introduce conditional traffic rates for arrivals and departures. Using them, we consider when the network has product form or some other tractable stationary distributions.  相似文献   

15.
Majewski  Kurt 《Queueing Systems》2004,48(1-2):103-134
We investigate large deviations for the behavior of single class queueing networks. The starting point is a sample large deviation principle on the path-space of network primitives describing the cumulative external arrivals, service time requirements and routing decisions. The behavior of the network, capturing the cumulative total arrivals, idle times and queue lengths, is characterized by a path-space fixed point equation containing the network primitives. The mapping from the network primitives to the set of fixed points is partially upper semicontinuous. This set-valued continuity allows us to derive large deviation bounds for the network behavior in the form of variational problems. The analysis is carried out on the doubly-infinite time axis R and can directly capture stationary and non-Markovian situations. By relaxing the fixed point equation the upper bounds and minimizing paths can be approximated with piecewise linear paths. For a class of typical rate functions we specify sequences of finite dimensional minimization problems which permit the calculation of large deviation rates and minimizing paths for the tail probabilities of queue lengths. We illustrate the approach with an example.  相似文献   

16.
This paper develops a game theory model of a service-oriented Internet in which profit-maximizing service providers provide substitutable (but not identical) services and compete with the quantities of services in a Cournot–Nash manner, whereas the network transport providers, which transport the services to the users at the demand markets, and are also profit-maximizers, compete with prices in Bertrand fashion and on quality. The consumers respond to the composition of service and network provision through the demand price functions, which are both quantity and quality dependent. We derive the governing equilibrium conditions of the integrated game and show that it satisfies a variational inequality problem. We then describe the underlying dynamics, and provide some qualitative properties, including stability analysis. The proposed algorithmic scheme tracks, in discrete-time, the dynamic evolution of the service volumes, quality levels, and the prices until an approximation of a stationary point (within the desired convergence tolerance) is achieved. Numerical examples demonstrate the modeling and computational framework.  相似文献   

17.
Stochastic loss networks are often very effective models for studying the random dynamics of systems requiring simultaneous resource possession. Given a stochastic network and a multi-class customer workload, the classical Erlang model renders the stationary probability that a customer will be lost due to insufficient capacity for at least one required resource type. Recently a novel family of slice methods has been proposed by Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407–418, 2008) to approximate the stationary loss probabilities in the Erlang model, and has been shown to provide better performance than the classical Erlang fixed point approximation in many regimes of interest. In this paper, we propose some new methods for loss probability calculation. We propose a refinement of the 3-point slice method of Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407–418, 2008) which exhibits improved accuracy, especially when heavily loaded networks are considered, at comparable computational cost. Next we exploit the structure of the stationary distribution to propose randomized algorithms to approximate both the stationary distribution and the loss probabilities. Whereas our refined slice method is exact in a certain scaling regime and is therefore ideally suited to the asymptotic analysis of large networks, the latter algorithms borrow from volume computation methods for convex polytopes to provide approximations for the unscaled network with error bounds as a function of the computational costs.  相似文献   

18.
Mathematical Notes - We study a feedback optimal control problem for a three-dimensional model of a stationary flow of a non-Newtonian fluid (with variable viscosity) in a pipeline network with...  相似文献   

19.
提出吸引度依赖于时间的竞争网络模型.利用Poisson过程获得这个模型稳态平均度分布的解析表达式.理论分析表明,这类网络幂律指数与渐近吸引系数和新节点边数m有关,且在区间(1+1/m,m+1)内.作为竞争网络模型的应用,获得了适应度模型的度分布估计.结果表明适应度模型是竞争网络模型的特例,反之则不然.  相似文献   

20.
We review two areas of recent research linking proportional fairness with product form networks. The areas concern, respectively, the heavy traffic and the large deviations limiting regimes for the stationary distribution of a flow model, where the flow model is a stochastic process representing the randomly varying number of document transfers present in a network sharing capacity according to the proportional fairness criterion. In these two regimes we postulate the limiting form of the stationary distribution, by comparison with several variants of the fairness criterion. We outline how product form results can help provide insight into the performance consequences of resource pooling.  相似文献   

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