串联系统可靠性虚拟系统法置信下限的小样本性质

本文讨论了具有r个成败型元件串联系统可靠性的置信下限问题。研究了虚拟系统法置信下限的小样本性质,证明了,在通常情况下虚拟系统法置信下限要大于常见的L-M法置信下限.更一般地,本文证明了在成败型试验中,当成功数与试验数之比保持不变时,试验次数的增加将直接缩小成功率置信区间的长度。     

一类几乎最优循环图{C_p(m,m+1,p/a)}

本文比较了循环图类{c_p(n_1,…,n_p)}和{c-p(n_1…,n_p,p/α)}的直径下界。对于p和α满足一定条件的循环图类{c_p(n_1,n_2,p/α)},本文给出了达到或几乎达到此图类直径下界的一类几乎最优循环图{c_p(m,m+1,p/α)}。     

等式与界约束非线性优化信赖域算法的全局收敛

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ :ｍｉｎｉｍｉｚｅｆ(ｘ)ｓｕｂｊｅｃｔｔｏＣ(ｘ) =0 ,　ａ≤ｘ≤ｂ ,( 1 .1 )ｗｈｅｒｅｆ(ｘ) :Ｒｎ→Ｒ ,Ｃ(ｘ) =(ｃ1(ｘ) ,ｃ2 (ｘ) ,...,ｃｍ(ｘ) ) Ｔ:Ｒｎ→Ｒｍ ａｒｅｔｗｉｃｅｃｏｎｔｉｎｕｏｕｓｌｙｄｉｆｆｅｒｅｎｔｉａｂｌｅ,ｍ≤ｎ ,ａ ,ｂ∈Ｒｎ.Ｔｒｕｓｔｒｅｇｉｏｎａｌｇｏｒｉｔｈｍｓａｒｅｖｅｒｙｅｆｆｅｃｔｉｖｅｆｏｒｓｏｌｖｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉ…     

Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms

We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions.     

Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given. This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Computational Sciences of Shanghai Universities. An erratum to this article is available at .     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

大规模界约束优化的子空间截断牛顿法

给出了大规模界约束优化的一个子空间截断牛顿法。利用截断牛顿法修正非有效约束所对应的变量，用投影梯度法修正有效约束所对应的变量，文中证明了方法的整体收敛性，并对方法进行了数值试验，且与子空间有限内存拟牛顿法进行了数值比较。     

On error bounds for lower semicontinuous functions

We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f. In a reflexive Banach space X, we further obtain several sufficient and necessary conditions for the existence of error bounds in terms of the lower Dini derivative of f. Received: April 27, 2001 / Accepted: November 6, 2001?Published online April 12, 2002     

离散大系统解的有界性与周期解的存在性

本文分别利用向量Ｌｙａｐｕｎｏｖ函数方法和标量Ｌｙａｐｕｎｏｖ函数方法，给出了判定离散大系统解的有界性与周期解的存在性的充分条件，并讨论了一类具有非线性时变周期离散大系统的平稳振荡存在性问题．