下层带扰动参数的二层多目标最优化问题有效点集的锥次微分稳定性

关于集值映射最优化问题有效点集的稳定性问题,一些学者在半连续意义下得到比较系统的结果。近年,在锥次微分意义下又获得更深入的描述。借助集值映射最优化问题有效解(点)的锥次微分稳定性理论,讨论了上层无扰动,下层带扰动参数的二层多目标最优化问题有效点集的锥次微分稳定性。     

分布式通信响应优化问题及其内点法求解

为了优化移动互联网的分布式通信系统的响应速度,建立分布式通信系统响应速度最优化问题的数学模型,并设计和改进求解该最优化问题的内点法.针对该最优化问题发展一套高效率预条件方法来帮助求解内点法,不但改善计算方法的数值稳定性,而且提高算法的计算效率.通过数值实验验证该预条件对算法稳定性和效率的提高.     

最优化方法课程思政探索与实践

立德树人是高校的根本任务,课程思政建设势在必行.本文以最优化方法这门本科生专业课程开展的思政教学改革方面的经验为例,从课程思政教学目标设计、教学内容体系开发、教学方法设计与实施以及教学效果四个方面详细阐述了如何建设一门有专业特色的课程思政课程,为培养德才兼备的高素质人才做出贡献.     

无正则性条件下的一个信赖域方法的全局收敛性

1.引 言考虑下列等式约束最优化问题:min f(x)x∈Rn (1.1)s.t.C(x)=0其中f:Rn→R,C（x）=（c1（x）,C2（x）,…,Cm（x））T,Ci:Rn→R,（i=1,…,m）.我们假设f（x）,Ci（x）（i=1,2,…,m）是连续可微函数.令g（x）=　f（x）,A（x）=　C（x）T.为了方便,我们通常用 Ck,fk,gk,Ak分别表示 C（xk）,f（xk）,g（xk）A（xk）. SQP方法是一迭代方法.在 xk点,通过解下列子问题来得到搜索方向 dk     

求解多项式规划的一个全局最优化算法

提出一个求解带箱子约束的一般多项式规划问题的全局最优化算法, 该算法包含两个阶段, 在第一个阶段, 利用局部最优化算法找到一个局部最优解. 在第二阶段, 利用一个在单位球上致密的向量序列, 将多元多项式转化为一元多项式, 通过求解一元多项式的根, 找到一个比当前局部最优解更好的点作为初始点, 回到第一个 阶段, 从而得到一个更好的局部最优解, 通过两个阶段的循环最终找到问题的全局最优解, 并给出了算法收敛性分析. 最后, 数值结果表明了算法是有效的.     

培养学生发散思维能力的实践

所谓"发散思维",是指从问题的多种可能方向扩散出去,探索问题的多种解决方案的一种思维活动.从不同方向、不同角度进行多向联想,开阔思维视野,寻求问题的最优化解法,是发散思维的具体表现.发散思维具有多向性、独立性、运动性和探索性等特征,它在创新思维活动中占有主导地位.重视发散性思维的训练,对培养"创新型"人才具有十分重要的意义.     

Improved nonlinear optimization in the storage ring of the modern synchrotron radiation light source

In the storage ring of the third generation light sources, nonlinear optimization is an indispensable course in order to obtain ample dynamic acceptances and to reach high injection efficiency and long beam lifetime, especially in a low emittance lattice. An improved optimization algorithm based on the single resonance approach, which takes relative weight and initial Harmonic Sextupole Integral Strength （HSIS） as search variables, is discussed in this paper. Applications of the improved method in several test lattices are presented. Detailed analysis of the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF） is particularly emphasized. Furthermore, cancellation of the driving terms is investigated to reveal the physical mechanism of the harmonic sextupole compensation. Sensitivity to the weight and the initial HSIS as well as dependence of the optimum solution on the convergent factor is analyzed.     

基于随机搜索的一个约束优化问题的全局收敛算法

讨论了具有一般约束的全局优化问题,给出该问题的一个随机搜索算法,证明了该算法依概率1收敛到问题的全局最优解．数值结果显示该方法是有效的．     

Theoretical Study on a 42 T Model of Beta Zeolite by Density Functional Theory Simulation

Density functional theory was applied to study the structure of Beta zeolite. A model cluster containing 41Si atoms, 1 Al atom, 70 O atoms and 29 H atoms was constructed. The model structures were optimized using the Becke＇s three-parameter hybrid method with the Lee-Yang-Parr correlation functional （B3LYP） and the 6-31G basis set applying the Gaussian03 program package. The NMR parameters were calculated to validate the rationality of the model. It was found that in the optimization models, all O-H bond lengths were in range of 0.984-0.985A^°, among which the model with O-H bond length of 0.98478A^° was more stable than the others. The ^1H and ^27Al chemical shifts of the most stable model were 4.03434 and 55.74 ppm, which were pretty consistent with Larry＇ s experimental data of 4.1 and 54 ppm. The relationship between other structure parameters and total relative electric energy has also been found. All the results exhibit that the 42 T （the total number of Si and Al atoms is 42） model has common properties of the standard of zeolite Beta.     

一类新的非单调记忆梯度法及其全局收敛性

在非单调Armijo线搜索的基础上提出一种新的非单调线搜索,研究了一类在该线搜索下的记忆梯度法,在较弱条件下证明了其全局收敛性。与非单调Armijo线搜索相比,新的非单调线搜索在每次迭代时可以产生更大的步长,从而使目标函数值充分下降,降低算法的计算量。