Global convergence of conjugate gradient method

In this article, we consider the global convergence of the Polak–Ribiére–Polyak conjugate gradient method (abbreviated PRP method) for minimizing functions that have Lipschitz continuous partial derivatives. A novel form of non-monotone line search is proposed to guarantee the global convergence of the PRP method. It is also shown that the PRP method has linear convergence rate under some mild conditions when the non-monotone line search reduces to a related monotone line search. The new non-monotone line search needs to estimate the Lipschitz constant of the gradients of objective functions, for which two practical estimations are proposed to help us to find a suitable initial step size for the PRP method. Numerical results show that the new line search approach is efficient in practical computation.     

Optimal control of sources on some classes of functions

In this work, we investigate the problems of the control of sources’ motion and power, which influence the state of the objects described by partial differential equations. The functions defining the sources’ operation are taken from different classes of functions that are easy to implement from the technical point of view. For numerical solution to the problems considered, we obtain and validate formulae for the gradient of a target functional, which allow using first-order optimization methods, e.g. gradient projection method.     

Gradient differences and bilateral barters

Exchange is modelled here as iterated bilateral barters, each fairly myopic and driven merely by gradient differences. Under weak conditions, repeated transactions carry the economy to market equilibrium, supported by clearing prices. A main feature is that agents, in the interim, are allowed non-admissible, possibly speculative, but sharply penalized positions.     

Smoothing method in multi-criteria transportation network equilibrium problem

ABSTRACT

This paper is aimed to study a single-product multi-criteria transportation network with capacity constraints. We use a vector version of the Heaviside Step function to construct an optimization problem, the solutions of which form the set of equilibria of our model. We propose two methods to solve this problem. The first one is based on a modified Frank-Wolfe gradient algorithm, and the second one is based on smoothing the objective function, the optimal solutions of which can be obtained by optimization tools. Numerical examples are also given to illustrate our approaches.     

Nonlinear microbeam model based on strain gradient theory

The nonlinear governing equation of microbeam based on the strain gradient theory is derived by using a combination of the strain gradient theory and the Hamilton’s principle, and the nonlinear static bending deformation, the post-bucking problem and the nonlinear free vibration are analyzed. The nonlinear term in the nonlinear governing equation is associated with the mean axial extension of the microbeam. The static bending deformation of the clamped–clamped microbeam subjected to transverse force, the critical buckling loads and the nonlinear frequencies of the simple supported microbeam with initial lateral displacement are discussed. It is shown that the size effect is significant when the ratio of characteristic thickness to internal material length scale parameters is approximately equal to one or two, but is diminishing with the increase of the ratio. The results also indicate that the nonlinearity has a great effect on the static and dynamic behavior of microbeam. To attain accurate and reliable characterization of the static and dynamic properties of microbeam, therefore, both the micro structure dependent parameters and the nonlinear term have to be incorporated in the design of micro structures in MEMS or NEMS.     

大规模非线性互补问题的共轭梯度法

提出求解大规模非线性互补问题NCP(F)的PRP型共轭梯度法,算法自然满足充分下降条件.当F是可微P_0+R_0函数且F'(χ)在水平集上全局Lipschitz连续条件下,证明了算法的全局收敛性.数值结果表明算法的有效性.     

第一原理研究界面弛豫对InAs/GaSb超晶格界面结构、能带结构和光学性质的影响

通过广义梯度近似的第一原理全电子相对论计算, 研究了不同界面类型InAs/GaSb超晶格的界面结构、电子和光吸收特性. 由于四原子界面的复杂性和低对称性, 通过对InAs/GaSb超晶格进行电子总能量和应力最小化来确定弛豫界面的结构参数. 计算了InSb, GaAs型界面和非特殊界面(二者交替)超晶格的能带结构和光吸收谱, 考察了超晶格界面层原子发生弛豫的影响.为了证实能带结构的计算结果, 用局域密度近似和Hartree-Fock泛函的平面波方法进行了计算. 对不同界面类型InAs/GaSb超晶格的能带结构计算结果进行了比较, 发现界面Sb原子的化学键和离子性对InAs/GaSb超晶格的界面结构、 能带结构和光学特性起着至关重要的作用.     

快放电直线型变压器驱动源磁芯脉冲损耗特性

建立了快脉冲磁芯损耗特性测试平台,对比研究了50 m的DG6硅钢和25 m的2605TCA非晶两种材料磁芯损耗特性;采用一种新的特征参量(磁芯单位面积上激磁电压陡度)来规范磁芯的激磁电压条件,使得实验结果与快放电直线型变压器驱动源实际工作条件下磁芯性能具有可比性;通过测量初级漏电流及次级开路电压,获得了相同激磁条件下两种磁芯等效损耗电阻的大小,50 m 的DG6硅钢磁芯损耗约为25 m的2605TCA非晶磁芯损耗的4倍;计算了两种材料磁芯总损耗中涡流损耗所占的比例,50 m的DG6硅钢磁芯涡流损耗占总损耗的75%,25 m的2605TCA非晶磁芯涡流损耗占总损耗的28%。     

亚微秒脉冲下高梯度绝缘子的沿面闪络特性

介绍了一种由聚酰亚胺和不锈钢叠加而成的高梯度绝缘子的实验研究工作。该绝缘子样品的直径60 mm,厚度8 mm,在脉冲宽度120 ns(FWHM)的电压脉冲加载下最高获得了接近13 MV/m的绝缘强度。研究了测试方法以及绝缘层厚度与金属层厚度的比例对高梯度绝缘子绝缘强度的影响,并与相同尺寸的普通材料绝缘子的绝缘强度进行了对比。结果表明,高梯度绝缘子的绝缘强度明显高于仅由聚酰亚胺构成的普通绝缘子。