一种具有全局收敛性的求解二阶锥规划的非精确光滑算法

在方程组方法框架下,给出了一种求解二阶锥规划的非精确光滑算法.在适当的条件下,证明了该算法具有全局收敛性.数值试验表明该算法对求解中大规模二阶锥规划是有效的.     

非线性二阶锥互补问题的低阶罚函数算法（英文）

本文研究非线性二阶锥互补问题的一般低阶罚函数算法.并将非线性二阶锥互补问题转化为序列非线性方程组.在一定条件下,当罚因子趋向于无穷时,获得序列非线性方程组的解序列以指数速度收敛于原始非线性二阶锥互补问题的解,推广了幂罚函数算法求解非线性二阶锥互补问题的结果.数值实验结果说明了算法的有效性.     

二次锥规划的预估-校正光滑方法

基于光滑Fischer-Burmeister函数,给出一个求解二次锥规划的预估-校正光滑牛顿法.该算法构造一个等价于最优性条件的非线性方程组,再用牛顿法求解此方程组的扰动.在适当的假设下,证明算法是全局收敛且是局部二阶收敛的.数值试验表明算法的有效性.     

求解圆锥规划的光滑牛顿法

圆锥规划是一类重要的非对称锥优化问题.基于一个光滑函数,将圆锥规划的最优性条件转化成一个非线性方程组,然后给出求解圆锥规划的光滑牛顿法.该算法只需求解一个线性方程组和进行一次线搜索.运用欧几里得约当代数理论,证明该算法具有全局和局部二阶收敛性.最后数值结果表明算法的有效性.     

均衡约束为二阶锥约束广义方程的数学规划问题的二阶充分条件(英)

本文考虑一类均衡约束为二阶锥约束广义方程的数学规划问题. 我们通过一个非光滑映射的方向导数, 给出了临界锥的定义, 并建立它在可行点处的等价形式. 基于此临界锥, 我们提出了均衡约束为二阶锥约束广义方程的数学规划问题的二阶充分性条件, 并且验证了在适当的条件下, M-稳定点处的二阶充分性条件是二阶增长条件成立的充分条件.     

求解二阶锥绝对值方程组的非单调光滑牛顿算法

本文提出了求解二阶锥绝对值方程组(SOCAVE)的非单调光滑牛顿算法.在适当的条件下分析了算法的全局收敛性和局部二次收敛性.数值结果表明用非单调光滑牛顿算法求解SOCAVE是可行且高效的.     

线性二阶锥互补问题的一种非精确光滑算法

在光滑算法的框架下,就线性二阶锥互补问题,给出了一种非精确光滑算法. 在适当的条件下,证明了该算法具有全局收敛性. 数值试验表明该算法对高维线性二阶锥互补问题是有效的.     

一个求解二阶锥互补问题的非单调光滑算法

光滑算法是求解二阶锥互补问题非常有效的方法,而这类算法通常采用单调线性搜索.给出了一个求解二阶锥互补问题的非单调光滑算法,在不需要满足严格互补条件下证明了算法是全局和局部二阶收敛的.数值试验表明算法是有效的.     

一个求解二阶锥互补问题的非单调光滑算法北大核心

光滑算法是求解二阶锥互补问题非常有效的方法,而这类算法通常采用单调线性搜索.给出了一个求解二阶锥互补问题的非单调光滑算法,在不需要满足严格互补条件下证明了算法是全局和局部二阶收敛的.数值试验表明算法是有效的.     

一个求解二阶锥规划的光滑牛顿算法

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.     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.     

Connections between stability and asymptotic stability of nonlinear switched systems

Here are considered nonlinear switched systems in which the switching occurs among a class of subsystems that are characterized by input–output properties stated in terms of L_p spaces of signals. The relationships between the L_p stability of each subsystem and the internal stability of the switched system are studied. In particular, conditions on the dwell time of the switching signals that guarantee the asymptotic stability of the overall system are provided. The connections among these conditions and the L_p input–output properties of the subsystems are investigated.     

非自治p(t)-拉普拉斯系统周期解的存在性

本文研究一类非自治p(t)-Laplace系统.利用鞍点定理和极小作用原理,获得了周期解存在的充分条件,推广和改进了文献[8]中的结果.     

Truncated Lie groups and almost Klein models

We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M ^G . Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup.     

The M/G/c queue in light traffic

Under light traffic, we investigate the quality of a well‐known approximation for first‐moment performance measures for an M/G/c queue, and, in particular, conditions under which the approximation is either an upper or a lower bound. The approach is to combine known relationships between quantities such as average delay and time‐average work in system with direct sample‐path comparisons of system operation under two modes of operation: conventional FIFO and a version of preemptive LIFO. We then use light traffic limit theorems to show an inequality between time‐average work of the M/G/c queue and that of the approximation. In the process, we obtain new and improved approximations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Reconstructing Coefficients of Series from Certain Orthogonal Systems of Functions

We consider a series with respect to a multiplicative Price system or a generalized Haar system and assume that the martingale subsequence of its partial sums converges almost everywhere. In this paper we prove that, under certain conditions imposed on the majorant of this sequence, the series is a Fourier series in the sense of the A-integral (or its generalizations) of the limit function if the series is considered as a series with respect to a system with supp _n < . In similar terms, we also present sufficient conditions for a series to be a Fourier series in the sense of the usual Lebesgue integral. We give an example showing that the corresponding assertions do not hold if supp _n = .     

On the Existence of Elementary Abelian Cycle Systems

We present some necessary and/or sufficient conditions for the existence of an elementary abelian cycle system of the complete graph. We propose a construction for some classes of perfect elementary abelian cycle systems. Finally we consider elementary abelian k-cycle systems of the complete multipartite graph.      

Semiconvergence of block SOR method for singular linear systems with p-cyclic matrices

In this paper, we discuss semiconvergence of the block SOR method for solving singular linear systems with p-cyclic matrices. Some sufficient conditions for the semiconvergence of the block SOR method for solving a general p-cyclic singular system are proved.     

On the Existence of Periodic Solutions for a Nonlinear System of Ordinary Differential Equations

Abstract This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations. We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions Research supported by the NNSF of China and the RFDP of China.     

Fast formula of a reliability ofm-consecutive-k-out-of-n:F system with cyclek

Anm-consecutive-k-out-of-n:F system is a system ofn linearly arranged components which fails if and only if at leastm non-overlapping sequences ofk components fail, when there arek distinct components with failure probabilitiesq _i fori=1,...,k and where the failure probability of thej-th component (j=rk+i (1 ≤i ≤k) isq _j =q _i , we call this system by anm-consecutive-k-out-of-n:F system with cycle (or period)k. In this paper we give a formula of the failure probability ofm-consecutive-k-out-of-n:F system with cyclek via the failure probability of consecutive-k-out-of-n:F system.