一类特殊二维0-1规划的广义指派模型求解

二维0-1整数规划模型应用广泛,对广义指派问题的研究,解决了一些二维0-1整数规划问题.但有些实际问题具有特殊上限约束,目前还没有对应的方法.针对该实际情形,本文建立了相应的数学模型,利用对指派模型的推广,求得问题最优解,从理论上解决了这一类特殊约束二维0-1整数规划的最优解求取问题.并通过算例说明了方法的使用.     

Disintegration of Gaussian measures and average-case optimal algorithms

It is shown that a Gaussian measure in a given infinite-dimensional Banach space always admits an essentially unique Gaussian disintegration with respect to a given continuous linear operator. This covers a similar statement made earlier in [Lee and Wasilkowski, Approximation of linear functionals on a Banach space with a Gaussian measure, J. Complexity 2(1) (1986) 12–43.] for the case of finite-rank operators.     

A policy iteration algorithm for fixed point problems with nonexpansive operators

The aim of this paper is to solve the fixed point problems:

On stable least squares solution to the system of linear inequalities

The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable and degenerate problems primarily.      

L p -dual Quermassintegral sums

In this paper, we first introduce a concept of L _p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L _p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L _p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

Robust Dynamics and Control of a Partially Observed Markov Chain

In a seminal paper, Martin Clark (Communications Systems and Random Process Theory, Darlington, 1977, pp. 721–734, 1978) showed how the filtered dynamics giving the optimal estimate of a Markov chain observed in Gaussian noise can be expressed using an ordinary differential equation. These results offer substantial benefits in filtering and in control, often simplifying the analysis and an in some settings providing numerical benefits, see, for example Malcolm et al. (J. Appl. Math. Stoch. Anal., 2007, to appear). Clark’s method uses a gauge transformation and, in effect, solves the Wonham-Zakai equation using variation of constants. In this article, we consider the optimal control of a partially observed Markov chain. This problem is discussed in Elliott et al. (Hidden Markov Models Estimation and Control, Applications of Mathematics Series, vol. 29, 1995). The innovation in our results is that the robust dynamics of Clark are used to compute forward in time dynamics for a simplified adjoint process. A stochastic minimum principle is established.     

带鳍通道性能的遗传算法优化

与光滑通道相比,带鳍通道有更高的传热系数,附加的鳍,极大地增强了通道的传热.然而,传热的增强又与压降的升高相关联,这又导致泵动力需求的增加,因此应该寻求对该系统的优化设计.该文的主要目的是,通过如下方式来精确地确定鳍的位置和尺寸:利用遗传算法实现最小压降时达到最优传热.鳍的每种布局作为问题(遗传算法中的一个个体)的一个解.通常,首先随机地产生一个初始种群,然后该算法在所有这些解中搜索,利用布局函数迭代出新解,最后得到鳍的优化设计.     

二层线性规划的自适应遗传算法

提出了一种自适应遗传算法来求解二层线性规划问题.该方法克服了难以确定合适的交叉概率和变异概率的困难.另外,在该方法中还采用了其它一些技巧不仅解决了在采用遗传算法经常出现的有些个体不可行的问题,而且还改进了算法的效率.     

Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces

Let C be a closed convex subset of a real Hilbert space H and assume that T is a κ-strict pseudo-contraction on C with a fixed point, for some 0?κ<1. Given an initial guess x₀∈C and given also a real sequence {αn} in (0,1). The Mann's algorithm generates a sequence {xn} by the formula: xn+1=αnxn+(1−αn)Txn, n?0. It is proved that if the control sequence {αn} is chosen so that κ<αn<1 and , then {xn} converges weakly to a fixed point of T. However this convergence is in general not strong. We then modify Mann's algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence. This result extends a recent result of Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379] from nonexpansive mappings to strict pseudo-contractions.     

Greedy expansions in Banach spaces

We study convergence and rate of convergence of expansions of elements in a Banach space X into series with regard to a given dictionary . For convenience we assume that is symmetric: implies . The primary goal of this paper is to study representations of an element f∈X by a series