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.     

Guided waves in a monopile of an offshore wind turbine

We study the guided waves in a structure which consists of two overlapping steel plates, with the overlapping section grouted. This geometry is often encountered in support structures of large industrial offshore constructions, such as wind turbine monopiles. It has been recognized for some time that the guided wave technology offers distinctive advantages for the ultrasonic inspections and health monitoring of structures of this extent. It is demonstrated that there exist advantageous operational regimes of ultrasonic transducers guaranteeing a good inspection range, even when the structures are totally submerged in water, which is a consideration when the wind turbines are deployed off shore.     

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.     

Polynomiality of an inexact infeasible interior point algorithm for semidefinite programming

In this paper we present a primal-dual inexact infeasible interior-point algorithm for semidefinite programming problems (SDP). This algorithm allows the use of search directions that are calculated from the defining linear system with only moderate accuracy, and does not require feasibility to be maintained even if the initial iterate happened to be a feasible solution of the problem. Under a mild assumption on the inexactness, we show that the algorithm can find an -approximate solution of an SDP in O(n²ln(1/)) iterations. This bound of our algorithm is the same as that of the exact infeasible interior point algorithms proposed by Y. Zhang.Research supported in part by the Singapore-MIT alliance, and NUS Academic Research Grant R-146-000-032-112.Mathematics Subject Classification (1991): 90C05, 90C30, 65K05     

Scheduling electric power production at a wind farm

We present a model for scheduling power generation at a wind farm, and introduce a particle swarm optimization algorithm with a small world network structure to solve the model. The solution generated by the algorithm defines the operational status of wind turbines for a scheduling horizon selected by a decision maker. Different operational scenarios are constructed based on time series data of electricity price, grid demand, and wind speed. The computational results provide insights into management of a wind farm.     

微分方程解的存在区间的确定

从六个方面说明了确定一阶微分方程解的存在区间的方法.