求解P0线性互补问题的一种二次收敛不精确光滑牛顿方法

在FB函数的基础上,对P0线性互补问题给出了一种新的不精确光滑算法.新的算法对于相应的线性方程组只求其非精确解.在没有严格互补假设的条件下,新算法具有全局收敛和局部二次收敛的性质.数值试验表明算法对于求解大规模P0线性互补问题是非常有效的.     

线性权互补问题的改进全牛顿步不可行内点算法

权互补问题是指在一个流形与一个锥的交集上找到一向量对,使得这对向量的某代数积等于一个给定的权向量。当权向量为零时,权互补问题退化为互补问题。作为互补问题的非平凡推广,权互补问题可用于求解科学、经济和工程中的诸多均衡问题,且在某些情况下可以产生更高效的算法。考虑非负象限上的一类线性权互补问题,提出了一种改进的全牛顿步不可行内点算法来求其数值解。通过推广线性优化的全牛顿步不可行内点算法,给出了线性权互补问题的扰动问题、中心路径及其诱导的牛顿方向。算法构造了线性权互补问题的一系列扰动问题的严格可行点;每一步主迭代由一个可行步和若干个中心步组成,且都采用全牛顿步,因而无需计算步长;在每一步迭代,算法的可行性残差和权向量残差都以相同比率减少;运用中心步的二次收敛结果,为可行步提供了一个稍宽的邻域。通过分析算法的可行步,中心步和收敛性,得到了算法的全局收敛性和多项式时间复杂度。最后,数值算例验证了算法求解线性权互补问题的有效性。     

绝对值方程的一种新的半光滑牛顿法(英文)

绝对值方程产生于求解区间线性方程组,其定义为Ax|x|=b,其中A为n阶实矩阵.线性互补问题可以转化为一个绝对值方程,因此许多重要的数学规划问题可以转化为绝对值方程.本文基于min-函数和FB-函数,提出了求解绝对值方程的半光滑牛顿算法.该算法在每一次迭代中只需要求解一个线性方程组.当区间矩阵[A I,A+I]正则时,该算法全局收敛且有限步收敛;即任意给定初始点x0∈Rn,算法在有限次迭代之后收敛于绝对值方程的解.数值实验表明了算法的有效性,特别是大规模问题求解中的适用性.     

求解互补问题的原始对偶起作用集算法

在本文中我们得到了求解带T-单调算子的互补问题的原始对偶活跃集算法的收敛结果.当原始对偶活跃集算法求解此类互补问题时,此算法可以作为一类特殊的半光滑牛顿法.收敛结果和数值试验说明了此算法的迭代次数不超过问题未知数的个数.最终,计算结果表明此算法的可行性.     

求解垂直互补问题的一种修正非光滑Levenberg-Marquardt算法

本文提出了一种求解垂直互补问题的修正非光滑Levenberg-Marquardt算法.与以往算法相比,该算法不但采用了新的微分形式取代了B-微分,还运用了一种LM参数的自适应调整策略以确保每次迭代时LM步不至于过小,从而保证了算法的快速收敛.最后,数值实验表明了算法的有效性.     

不精确高斯——牛顿法的收敛性

考虑非解非线性最小二乘问题的不精确高斯－牛顿法。给出了在高斯－牛顿方程组不精确求解条件下，搜索方向Ｓ＾（ｎ）是下降和确保方法收敛的条件，文章还证明了，如果高斯－牛顿方程组的求解是渐近精确的，则对充分大的Ｋ，步长ａｋ＝１是可接受的，且方法的局部收敛率是超线性的。     

求解垂直互补问题的一种修正非光滑Levenberg-Marquardt算法（英文）

本文提出了一种求解垂直互补问题的修正非光滑Levenberg-Marquardt算法.与以往算法相比,该算法不但采用了新的微分形式取代了B-微分,还运用了一种LM参数的自适应调整策略以确保每次迭代时LM步不至于过小,从而保证了算法的快速收敛.最后,数值实验表明了算法的有效性.     

Mohr-Coulomb准则角点问题的主应力空间互补算法

Mohr-Coulomb准则由于角点问题的存在导致其在数值计算时收敛困难,首先阐述了其角点问题的实质是主应力随罗德角的变化而不光滑导致的,然后给出了主应力空间法的理论基础,最后基于Koiter法则在主应力空间将Mohr-Coulomb准则的多屈服面表达为其等价的互补模型,并进一步用Fischer-Burmeister互补函数进行描述,从而使得牛顿算法可以顺利地进行求解。所提出的算法解决了Mohr-Coulomb准则中的角点问题,避免了常规方法的试算过程,提高了Mohr-Coulomb准则的精度。算例验证了该方法的有效性和可靠性。     

基于线性互补问题的多体系统接触/碰撞动力学研究

多体系统往往包含大量的接触/碰撞行为,这些非光滑事件的存在造成了动力学方程的不连续或分段连续,给数值求解带来了很大的困难。为综合考虑平顺接触与碰撞,采用基于线性互补问题的非光滑动力学方法,首先在当前时刻为起点的短时间内对对缝隙函数进行均匀化,然后与法向接触力建立标准线性互补方程,最后将线性互补方程改造为一组非线性代数方程,通过非线性迭代可直接求解接触力。算例结果表明,采用该方法不需在接触状态发生改变时切换模型,且严格满足互补关系,保证了接触力的非负性。研究成果可成为求解多柔体系统接触/碰撞问题的新途径。     

拉压不同模量材料的参变量变分原理和有限元方法

对具有拉伸和压缩不同模量的材料,建立了平面静力问题的参变量变分原理.基于参变量变分原理,并结合有限元方法,将拉压不同模量平面问题转化为互补问题求解.经典的Lemke算法被用于求解此互补问题.该方法避免了应力状态的假设和刚度矩阵的更新,算法稳定,且收敛速度快.     

用工业工程思想发现、解决和预防问题

在工厂现场问题研究的基础上,联系生活实际,对问题科学进行了研究.定义了什么叫问题;探讨了问题的本质;对工作生活中问题进行了分类;阐明了问题和风险以及问题和矛盾之间的关系.利用工业工程(IE)的思想,分析了普遍的如何发现问题及解决问题的思维过程;阐明了在工作和生活中如何利用问题的实质去发现问题,并最终解决和预防问题.报告了解决问题的三个原则、注意事项和步骤.     

Pre‐college Electrical Engineering Instruction: The Impact of Abstract vs. Contextualized Representation and Practice on Learning

Background While engineering instructional materials and practice problems for pre‐college students are often presented in the context of real‐life situations, college‐level texts are typically written in abstract form. Purpose (Hypothesis ) The goal of this study was to jointly examine the impact of contextualizing engineering instruction and varying the number of practice opportunities on pre‐college students' learning and learning perceptions. Design/ Method Using a 3 × 2 factorial design, students were randomly assigned to learn about electrical circuit analysis with an instructional program that represented problems in abstract, contextualized, or both forms, either with two practice problems or four practice problems. The abstract problems were devoid of any real‐life context and represented with standard abstract electrical circuit diagrams. The contextualized problems were anchored around real‐life scenarios and represented with life‐like images. The combined contextualized‐abstract condition added abstract circuit diagrams to the contextualized representation. To measure learning, students were given a problem‐solving near‐transfer post‐test. Learning perceptions were measured using a program‐rating survey where students had to rate the instructional program's diagrams, helpfulness, and difficulty. Results Students in the combined contextualized‐abstract condition scored higher on the post‐test, produced better problem representations, and rated the program's diagrams and helpfulness higher than their counterparts. Students who were given two practice problems gave higher program diagram and helpfulness ratings than those given four practice problems. Conclusions These findings suggest that pre‐college engineering instruction should consider anchoring learning in real‐life contexts and providing students with abstract problem representations that can be transferred to a variety of problems.     

Airline planning and scheduling: Models and solution methodologies

The airline industry is a representative industry with high cost and low profitability. Therefore, airlines should carefully plan their schedules to ensure that overall profit is maximized. We review the literature on airline planning and scheduling and focus on mathematical formulations and solution methodologies. Our research framework is anchored on three major problems in the airline scheduling, namely, fleet assignment, aircraft routing, and crew scheduling. General formulation, widely used solution approaches, and important extensions are presented for each problem and integrated problems. We conclude the review by identifying promising areas for further research.     

Thermal deformation in a thin circular plate due to a partially distributed heat supply

In this paper, we develop an integral transform to determine temperature distribution in a thin circular plate, subjected to a partially distributed and axisymmetric heat supply on the curved surface, and study the thermal deformation. The results, obtained in series form in terms of Bessel’s functions, are illustrated numerically.     

Inverse problem of controlling the interface velocity in Stefan problems by conjugate gradient method

Abstract

The conjugate gradient method of minimization with adjoint equation is used successfully to solve the inverse problem in estimating an appropriate boundary control function such that the phase front moves at a desired velocity in the Stefan problem.

It is assumed that no prior information is available on the functional form of the unknown control function, therefore, it is classified as the function estimation in inverse calculation. The stability and accuracy of the inverse analysis using present algorithm are examined by comparing the results of the previous work by Voller [12].

Results show that the estimated control function by using conjugate gradient method did not exhibit oscillatory behavior in the inverse calculations for a broad range of front velocity while in [12] the inverse solutions are very sensitive to phase front velocity, therefore the application of future time stepping [2] is necessary in [12].

The advantage of applying this algorithm in inverse analysis lies in its stability as compared to the conventional minimization process [12]. Artificial future time stepping is unnecessary during the inverse calculation, since it is still an uncertainty in the inverse analysis. Furthermore, the inverse solutions obtained by the present method are found to be more accurate than the solutions obtained by the conventional minimization process.     

压电材料变分原理逆问题的研究——动力学中的逆问题

研究了压电材料耦合动态场中Hamilton 型和Gurtin 型变分原理的逆问题。采用变积方法, 建立了各级变分原理和广义变分原理, 为建立横观各向同性压电材料的动力学有限元分析模型提供了依据。      

Selecting and assessing challenge problems

Abstract

Organisations conducting research programs often focus the work of their scientists and technologists on challenge problems (CPs). These challenges are designed to ensure that progress is measurable and relevant to the goals of the program sponsor. Generating and selecting pertinent CPs is difficult, as is assessing their value. We describe a method of generating and selecting CPs and its application in a highly collaborative, multi-organisation research program. Thirty-eight biologists, chemists, mathematicians and computer scientists across academic, commercial and government organisations generated and ranked their top choices from among 12 richly described candidate challenge problems. A ranked-choice voting formula was applied. Five CPs were highly scored; the remaining seven were distributed across a lower range of scores. The program sponsor subsequently directed researchers to address six CPs, including the elected five. Analysis of the rationales that participants offered for their CP rankings revealed four domain-independent dimensions of value: capability, speed, impact and synergy. These dimensions of value can help managers of interdisciplinary research programs systematically select a portfolio of CPs that will efficiently apply utilise resources towards program goals and facilitate measurement of scientific progress.     

特殊圈上的逆1-maxian问题

逆1-maxian问题主要研究如何在一定的预算下修改网络中边的长度,使得其他所有顶点到预先给定顶点的距离之和尽可能的大.研究了特殊4-圈上的逆1-maxian问题,得到了该问题在任意预算下的最优解.然后,将问题推广到特殊n-圈的情形.最后,得到Hamming距离下特殊n-圈情形的一个最优解.