Efficient interval partitioning for constrained global optimization

A new efficient interval partitioning approach to solve constrained global optimization problems is proposed. This involves a new parallel subdivision direction selection method as well as an adaptive tree search. The latter explores nodes (intervals in variable domains) using a restricted hybrid depth-first and best-first branching strategy. This hybrid approach is also used for activating local search to identify feasible stationary points. The new tree search management technique results in improved performance across standard solution and computational indicators when compared to previously proposed techniques. On the other hand, the new parallel subdivision direction selection rule detects infeasible and suboptimal boxes earlier than existing rules, and this contributes to performance by enabling earlier reliable deletion of such subintervals from the search space.     

Conjugate directions method for solving interval linear systems

We propose the interval version of the conjugate directions method, to solve the problem of linear systems, with symmetric and positive definite interval matrix A, and a right-hand side interval vector b. This revised version was published online in June 2006 with corrections to the Cover Date.     

Adaptive nonmonotone line search method for unconstrained optimization

In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration, the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some numerical results which show the efficiency of the new algorithm are reported.      

亚纯函数涉及小函数的奇异方向

本文研究了平面上亚纯函数的奇异方向.利用角域内Ahlfors-Shimize特征函数和几个已有的关于函数增长性估计的引理,证明了复平面上的零级超越亚纯函数存在一条涉及小函数的T方向.推广了吴昭君和孙道椿给出的结果.     

测算具有方向技术效率的DEA方法

本文总结了现有技术效率的主要测算方法，借鉴定向技术距离函数思想，结合DEA思路，提出了一种新的用于技术效率指数测算的模型，并进一步探讨了如何识别决策单元的技术有效性和如何改进非技术有效决策单元的问题．着重分析了该技术效率指数模型与L型技术效率指数的关系，指出该模型是L型技术效率指数模型的一般形式．     

Magnetostriction and spin reorientation in ferromagnetic Laves phase Pr(Ga_xFe_(1-x))_(1.9) compounds

The magnetostriction, magnetization, and spin reorientation properties in Pr(Ga_xFe_(1-x))_(1.9) alloys have been investigated by high-precision x-ray diffraction(XRD) step scanning, magnetization, and Mo¨ssbauer spectra measurements. Ga substitution reduces the magnetostriction(λ_(||)) with magnetic field H ≥ 8 kOe(1 Oe = 1.33322×10~2 Pa), but it also increases the λ|| value when H ≤ 8 kOe at 5 K. Spin-reorientations(SR) are observed in all the alloys investigated, as determined by the step scanned XRD, Mo¨ssbauer spectra, and the abnormal temperature dependence of magnetization. An increase of the spin reorientation temperature(T_(SR)) due to Ga substitution is found in the phase diagram, which is different from the decrease one in many R(T_x Fe_(1-x))_(1.9)(T = Co, Al, Mn) alloys. The present work provides a method to control the easy magnetization direction(EMD) or T_(SR) for developing an anisotropic compensation system.     

风场影响下直接空冷系统热风回流率的空间分布特性

环境风场影响下,电站直接空冷系统热风回流加剧,传热性能恶化。掌握风场作用下直接空冷系统热风回流率的空间分布特性,可为空冷系统的设计和运行提供理论依据。以典型2×600 MW直接空冷电站为例,通过数值模拟获得了冷却空气流场和温度场,分别计算了空冷岛和各个空冷单元的热风回流率。计算结果表明,随环境风速增加,空冷岛热风回流率升高,并随风向发生显著变化,炉后来风时空冷岛热风回流最为严重。空冷单元热风回流率呈现空间分布特性,风场不同区域空冷单元热风回流存在显著差异,处于风场上游空冷单元通常具有更大的热风回流率。     

The fekete-szegö problem for close-to-convex functions with respect to the koebe function

An analytic function f   in the unit disk D :={z ∈ ? : |z| < 1}$\mathbb{D}\hspace{0.17em}:=\left\{z\hspace{0.17em}\in \hspace{0.17em}?\hspace{0.17em}:\hspace{0.17em}\left|z\right|\hspace{0.17em}<\hspace{0.17em}1\right\}$, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1−z)², z ∈ D$k\left(z\right)\hspace{0.17em}:=\hspace{0.17em}z/{\left(1-z\right)}^2,\hspace{0.17em}z\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$ if there exists δ∈(-π/2,π/2) such that Re{eiδ(1−z)²f^′(z)} > 0, ∈ D$\text{Re}\left\{{\text{e}}^{\text{i}\delta }{\left(1-z\right)}^2{f}^{\prime }\left(z\right)\right\}\hspace{0.17em}>\hspace{0.17em}0,\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szegö problem is studied.     

广义交替近似梯度算法的线性收敛分析

针对两个可分凸函数的和在线性约束下的极小化问题,在交替方向法的框架下,提出广义的交替近似梯度算法.在一定的条件下,该算法具有全局及线性收敛性.数值实验表明该算法有好的数值表现.