Confidence regional method of stochastic spanning tree problem

We consider a P model version of stochastic spanning tree problems with random edge costs. Parameters of underling probability distribution of edge costs are unknown and so they are estimated by a confidence region from statistical data. The problem is first transformed into a deterministic equivalent problem with a minimax type objective function and a confidence region of means and variances, since we assume normal distributions with respect to random edge costs. Our model reflects the situation that the maximum possible damage due to an unknown parameter should be minimized. We show the problem can be reduced to the deterministic equivalent problem of another stochastic spanning tree problem, which is already investigated by us. Thus, we can find an optimal spanning tree of the original problem very efficiently by this reduction.     

sdg IBM对稀土偶偶核基态形变的计算

用sdg IBM的内禀态,解析计算了稀土区的^152—164Dy、^154—168)Er、^170—186W、^168—194Os等偶偶同位素的基态形变,与其它理论及实验结果进行系统比较,表明sdg IBM能对核的形变作出很好的描述.     

Sequential estimation in regression models using analogues of trimmed means

A sequential procedure is proposed for constructing a fixed-size confidence region for the parameters of a linear regression model. The procedure is based on certain regression analogues of trimmed means, as formulated by Welsh (1987,Ann. Statist.,15, 20–36), rather than least squares estimates. For error distributions with continuous, symmetric density and some moment higher than fourth finite, if the design points of the model are bounded, then the procedure is both asymptotically consistent and asymptotically efficient as the size of the region approaches zero.Research supported in part by the National Science Foundation under Grants DMS 85-03321 and 88-02556 and by the Air Force under Grant AFOSR-87-0041.     

镉原子在He－Cd激光器冷凝区凝结的蒙特卡罗模拟

用蒙特卡罗方法模拟了镉原子在Ｈｅ—Ｃｄ激光器的两种结构不同的冷凝区内的凝结，得到了镉原子在结构不同的冷凝区凝结的分布关系，对两种结构的分布关系进行了比较，表明改进冷凝区的结构，可以提高冷凝区对镉原子的凝结率。     

Superlinear convergence of a trust region-type successive linear programming method

The convergence rate of the SLP method suggested in Ref. 1 is discussed for composite nondifferentiable optimization problems. A superlinear rate is assured under a growth condition, and it is further strengthened to a quadratic rate if the inside function is twice differentiable. Several sufficient conditions are given which make the growth condition true. These conditions can be relaxed considerably in practical use.This research was supported in part by the National Natural Science Foundation of China.The author is grateful to Professor E. Sachs, Universität Trier, Trier, West Germany, for his helpful suggestions.     

An efficient trust region method for unconstrained discrete-time optimal control problems

Discrete-time optimal control (DTOC) problems are large-scale optimization problems with a dynamic structure. In previous work this structure has been exploited to provide very fast and efficient local procedures. Two examples are the differential dynamic programming algorithm (DDP) and the stagewise Newton procedure—both require onlyO(N) operations per iteration, whereN is the number of timesteps. Both exhibit a quadratic convergence rate. However, most algorithms in this category do not have a satisfactory global convergence strategy. The most popular global strategy is shifting: this sometimes works poorly due to the lack of automatic adjustment to the shifting element.In this paper we propose a method that incorporates the trust region idea with the local stagewise Newton's method. This method possesses advantages of both the trust region idea and the stagewise Newton's method, i.e., our proposed method has strong global and local convergence properties yet remains economical. Preliminary numerical results are presented to illustrate the behavior of the proposed algorithm. We also collect in the Appendix some DTOC problems that have appeared in the literature.Partially supported by the Cornell Theory Center, which receives major funding from the National Science Foundation and IBM Corporation, with additional support from the State of New York and its Corporate Research Institutes; and by NSF, AFOSR, and ONR through grant DMS-8920550.     

On a subproblem of trust region algorithms for constrained optimization

We study a subproblem that arises in some trust region algorithms for equality constrained optimization. It is the minimization of a general quadratic function with two special quadratic constraints. Properties of such subproblems are given. It is proved that the Hessian of the Lagrangian has at most one negative eigenvalue, and an example is presented to show that the Hessian may have a negative eigenvalue when one constraint is inactive at the solution.Research supported by a Research Fellowship of Fitzwilliam College, Cambridge, and by a research grant from the Chinese Academy of Sciences.     

一类约束非光滑优化的非单调信赖域算法

提出了求解一类带一般凸约束的复合非光滑优化的信赖域算法 .和通常的信赖域方法不同的是 :该方法在每一步迭代时不是迫使目标函数严格单调递减 ,而是采用非单调策略 .由于光滑函数、逐段光滑函数、凸函数以及它们的复合都是局部Lipschitz函数 ,故本文所提方法是已有的处理同类型问题 ,包括带界约束的非线性最优化问题的方法的一般化 ,从而使得信赖域方法的适用范围扩大了 .同时 ,在一定条件下 ,该算法还是整体收敛的 .数值实验结果表明 :从计算的角度来看 ,非单调策略对高度非线性优化问题的求解非常有效     

基于演化的信赖域方法

把全局搜索性能优良的演人算法与具有总体收敛性能的信赖域算法相颌合形成局部随机搜索与全局确定性搜索相结合的演变信赖域,经具有适应性广，收敛性能好和收敛速度快的特点，为解决复杂的非线性优化问题提供了一种有效算法，并证明了算法的收敛性。