解P_0非线性互补问题的光滑Levenberg-Marquardt方法

本文研究了一个P0非线性互补问题.利用信赖域技术获得了求解该问题的光滑Levenberg-Marquardt算法,该算法在一定条件下具有全局性.利用局部误差界还获得了该算法的超线性和二次收敛.数值结果表明该算法是有效的.     

基于梯度投影的广义滤子填充函数方法

本文研究了约束非凸全局优化问题.利用滤子技术和填充函数的架构,提出了一个基于梯度投影的广义滤子填充函数算法,获得了较好的理论性质和数值效果.文章修改了填充函数的定义以及滤子技术的适用范围,推广了局部优化技术,使之成为约束全局问题的有效求解方法之一.     

水面舰船的数学船型

利用近似理论,提出船型曲线的带有形状因子的指数函数近似,进而利用设计要求中的排水量和浮心纵坐标,构造超越方程组.通过求解形状因子,得到船体型线的数学表达,获得满足静水性条件的初始船型,从而实现舰船的全参数化设计.技术利用舰船主尺度获得舰船初始船型,有助于舰船的概要设计和利用多学科设计优化技术.实例验证了方法的有效性.     

图像去噪的混合正则化LSQR算法

本文研究了图像去模糊去噪问题.利用正则化技术结合Krylov子空间方法,提出了混合正则化LSQR算法.实验结果表明该算法有效改善了问题的不适定性,获得了逼真度较高的复原图像.     

Sobolev型方程Wilson元解的高精度分析

本文利用积分恒等式和插值后处理等技术对 Sobolev型方程 Wilson非协调有限元解进行了高精度算法分析 ,获得了解的超逼近性质和插值有限元解的整体超收敛 .在此基础上 ,运用外推与校正方法进一步获得了具有更高精度的近似解及后验误差估计 .     

嵌套技术扩散模型估计与落后地区的技术追赶

技术差距带来的技术扩散效应决定了区域间可能存在着技术收敛.在限制指数模型中,所有国家和地区将获得相同的技术进步率,在逻辑斯蒂模型中,人力资本水平成为制约技术收敛的条件.将Benhabib和Speigel(2005)的跨国技术收敛的实证研究工作推广到国内地区研究之中,分析了中国30个省区1990-2008年技术进步率的影响因素及收敛情况.实证研究结果表明,中国30个省区的技术进步率趋异.人力资本是促进地区自主创新和技术扩散的积极因素.     

Keller-Segel拋物系统解的爆破现象

本文研究了Keller-Segel拋物系统在Robin边界条件下解的爆破问题.利用微分不等式技术,推导了一个一阶微分不等式,并由此不等式获得了在R~3上Keller-Segel抛物系统解的爆破时间的下界.在一些适当的约束条件下,也获得了在R~N(N3)上Keller-Segel抛物系统爆破解显式下界     

延期支付与订购量相关的易腐产品库存决策模型

本文研究了延期支付与订购量相关的易腐产品库存决策的问题.在易腐率很小的情况下,利用二阶泰勒展开式、矩阵论及优化技术方法,获得了最优缺货时间、最优订购周期及最优零售价格解析解;并在易腐率比较大的情况下,利用内点算法,获得了零售商最优决策数值解.数值实验分析了各参数对最优决策的影响.     

鞅差序列加权和的几乎处处收敛(英文)

本文研究了一类鞅差序列加权和的收敛性的问题.利用一些基本不等式和截尾技术,获得了加权和的几乎处处收敛性,推广了关于独立同分布的随机变量序列的相关结果.     

一个求解无约束优化的ODE型混合方法

基于非单调技术,本文给出一种新的求解无约束优化的ODE型算法.该算法的特点是:每次迭代时只解一次线性方程组系统而获得试验步,然后采用改进的非单调线搜索获得下一个迭代点,从而避免了重复求解线性方程组,减少了算法的计算量.在合理的假设条件下,该算法被证明是全局收敛和局部超线性收敛的.数值试验证实了该算法的有效性.     

Numerical simulations of spalling tests in order to investigate material properties of UHPC

In order to evaluate the material composition of Ultra High Performance Concrete (UHPC), material properties such as dynamic tensile strength or fracture strength and also the fracture energy under impact loading are of significant importance. The use of a modified Hopkinson Bar enables the determination of the required data. On the basis of experimental investigations our contribution deals with the numerical finite element simulation of the Hopkinson Bar test. The propagation of stress waves is reproduced by means of a special time-integration scheme. We simulate the propagation of cracks by using adaptive cohesive elements including a corresponding separation law. The critical energy release rate (Griffith-energy) is calculated and compared to the values determined by experimental results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fracture toughness investigations on UHPC by spalling tests

Ultra High Performance Concrete (UHPC) is defined as a new generation of concrete which shows improved performance and higher strength than traditional concrete. This allows to realize slender and much more durable structures and in this way significantly reduces the required resources. Despite its huge potential in construction, technical information about this new type of material is still limited. This contribution presents investigations on the dynamic mechanical behavior and properties of UHPC specimens by spalling experiments. Two different recipes were used to compare the properties. Due to the special specimen geometry (slender cylindrical) a flowable consistency was required to enable a sufficient degassing of the mixtures. For the test, a Split Hopkinson Pressure Bar (SHPB) has been modified and used. A high speed photograph system was focused on the fragmentation process during the test. On the basis of these experiments the dynamic E-moduli as well as the dynamic tensile strength of the UHPC specimens were determined. By observation of the specific crack patterns on each tested specimen and corresponding times, the dynamic fracture energy is calculated. Numerical simulations also were performed and compared to the experimental result. It is concluded that the dynamic tensile strength of the UHPC increases at higher strain rates. The results of the current study provide technical information about fracture and dynamic behavior of UHPC and the obtained values could be used for future computational models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On variable-step relaxed projection algorithm for variational inequalities

Projection algorithms are practically useful for solving variational inequalities (VI). However some among them require the knowledge related to VI in advance, such as Lipschitz constant. Usually it is impossible in practice. This paper studies the variable-step basic projection algorithm and its relaxed version under weakly co-coercive condition. The algorithms discussed need not know constant/function associated with the co-coercivity or weak co-coercivity and the step-size is varied from one iteration to the next. Under certain conditions the convergence of the variable-step basic projection algorithm is established. For the practical consideration, we also give the relaxed version of this algorithm, in which the projection onto a closed convex set is replaced by another projection at each iteration and latter is easy to calculate. The convergence of relaxed scheme is also obtained under certain assumptions. Finally we apply these two algorithms to the Split Feasibility Problem (SFP).     

On the NP-hardness of deciding emptiness of the split closure of a rational polytope in the 0,1 hypercube

Split cuts are prominent general-purpose cutting planes in integer programming. The split closure of a rational polyhedron is what is obtained after intersecting the half-spaces defined by all the split cuts for the polyhedron. In this paper, we prove that deciding whether the split closure of a rational polytope is empty is NP-hard, even when the polytope is contained in the unit hypercube. As a direct corollary, we prove that optimization and separation over the split closure of a rational polytope in the unit hypercube are NP-hard, extending an earlier result of Caprara and Letchford.     

突然起动双圆柱绕流初期流场的研究

本文推广Bar Lev M.等人在1975年提出的求解突然起动单圆柱初期流场的方法,研究了双圆柱的相应问题,对流函数φ采用匹配渐近展开法求出直到二级近似的分析解。     

Algorithms for the Split Variational Inequality Problem

We propose a prototypical Split Inverse Problem (SIP) and a new variational problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse problem (e.g., a Variational Inequality Problem (VIP)), the image of which under a given bounded linear transformation is a solution of another inverse problem such as a VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.     

A note on branch-and-cut-and-price

In this paper, we propose a methodology for branch-and-cut-and-price when cuts and columns are generated simultaneously. The methodology is illustrated with two application cases: the Split Delivery Vehicle Routing Problem (SDVRP) and the Bus Rapid Transit Route Design Problem (BRTRDP).     

Multi-output dependent observability normal form

This article gives a sufficient condition which guarantees the existence of a reference frame in which a multi-output nonlinear system is linearizable with a linear part depending on its outputs. Our method is based on the design of a reference frame associated with nonlinear observable systems. Moreover, we give a generalization of the result obtained in [D. Boutat, G. Zheng, J.P. Barbot, Observer error linearization multi-output depending, in: Proc. of IEEE CDC 06, 2006] and [G. Zheng, D. Boutat, J.P. Barbot, Single output-dependent observability normal form, SIAM Journal on Control and Optimization 46 (6) (2007)]. And some examples are given in order to illuminate our thinking.     

Algorithms with new parameter conditions for split variational inclusion problems in Hilbert spaces with application to split feasibility problem

Split variational inclusion problem is an important problem, and it is a generalization of the split feasibility problem. In this paper, we present feasible algorithms for the split variational inclusion problems in Hilbert spaces, and provide convergence theorems for these algorithms. As application, we study the split feasibility problem in real Hilbert spaces. Final, numerical results are given for our main results.