A note on functional a posteriori estimates for elliptic optimal control problems

In this work, new results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed, and fully computable lower bounds for the cost functional in addition to the already existing upper bounds. Using both, the lower and the upper bounds, we arrive at two‐sided estimates for the cost functional. We prove that these bounds finally lead to sharp, guaranteed and fully computable upper estimates for the discretization error in the state and the control of the optimal control problem. First numerical tests are presented confirming the efficiency of the a posteriori estimates derived. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 403–424, 2017     

均衡约束数学规划问题的一种新的约束规格

本文研究了均衡约束数学规划(MPEC)问题.利用其弱稳定点,获得了一种新的约束规格–MPEC的伪正规约束规格.用一种简单的方式,证明了该约束规格是介于MPEC-MFCQ(即MPEC,Mangasarian-Fromowitz约束规格)与MPEC-ACQ(即MPEC,Abadie约束规格)之间的约束规格,因此该约束规格也可以导出MPEC问题的M-稳定点.最后通过两个例子,说明了该约束规格与MPEC-MFCQ以及与MPEC-ACQ之间是严格的强弱关系.     

一类具有资源约束和优先加工顺序约束极小化加权总完工时间调度优化问题研究

本文针对工件间具有链状优先约束和relocation资源约束的极小化加权总完工时间调度优化问题展开研究.针对这一NP难问题,利用relocation约束的性质和贪婪算法的思想,设计了一个多项式近似算法,并证明了当链不可中断,每个链具有相同工件数和工件间具有相同加工时间时,2为该算法的紧界.     

带1-范数约束的分裂可行问题的投影算法

本文主要研究带1-范数约束的分裂可行问题的求解算法.用一种交替投影算法,求得了问题的解,提出松弛交替投影算法,改进了直接往闭凸集上投影这一不足,并证明了该算法的收敛性.     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

正交约束优化问题的一阶算法

带有正交约束的矩阵优化问题在材料计算、统计及数据分析等领域中有着广泛的应用.由于正交约束的可行域是Stiefel流形,一直以来流形上的优化方法是求解这一问题的主要方法.近年来,随着实际应用问题所要求的变量规模的扩大,传统的流形优化方法在计算上的劣势显现出来,而一些迭代简单、收敛快的新算法逐渐被提出.通过收缩方法、非收缩可行方法、不可行方法三个类别分别来介绍求解带有正交约束的矩阵优化问题的最新算法.通过分析这些方法的主要特性,以及应用问题的要求,对这类问题算法设计的研究进行了展望.     

Semiparametric Bayesian inference for mean-covariance regression models

In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.     

Computational method for optimal control of switched systems with input and state constraints

In this paper, we consider an optimal control problem of switched systems with input and state constraints. Since the complexity of such constraint and switching laws, it is difficult to solve the problem using standard optimization techniques. In addition, although conjugate gradient algorithms are very useful for solving nonlinear optimization problem, in practical implementations, the existing Wolfe condition may never be satisfied due to the existence of numerical errors. And the mode insertion technique only leads to suboptimal solutions, due to only certain mode insertions being considered. Thus, based on an improved conjugate gradient algorithm and a discrete filled function method, an improved bi-level algorithm is proposed to solve this optimization problem. Convergence results indicate that the proposed algorithm is globally convergent. Three numerical examples are solved to illustrate the proposed algorithm converges faster and yields a better cost function value than existing bi-level algorithms.     

木质素热解生物油组成成分与分子尺寸分布特性分析

选用脱碱木质素作为原料,以热裂解气质联用技术(Py-GC/MS)研究木质素在350～600℃下热解产物成分和含量,并利用Joback法、 Lijie法和Tahami法3种基团贡献法计算了生物油各组成成分的临界参数和动力学直径,对木质素热解油产物的分子动力学直径分布特性进行计算.结果显示,愈创木基结构、紫丁香基结构、苯酚类、邻苯二酚类和芳烃类等5种芳香族化合物是350～600℃下木质素热解生物油的主要组成成分,其中愈创木基结构化合物的平均峰面积百分比达到70.7%.随着反应温度从350提高到600℃,分子动力学直径在0.560～0.610 nm区间内的木质素热解油组分含量从14.6%增加至31.3%.木质素热解生物油主要产物的动力学直径在0.560～0.710nm,表明一些孔径尺寸在此范围内的分子筛如SSZ-20、 ZSM-5和Beta可作为木质素裂解制备高品质芳烃燃料的催化剂.     

Preparation of modified multi‐walled carbon nanotubes as a reinforcement for epoxy shape‐memory polymer composites

Effectively improving the mechanical properties and thermal resistance of epoxy shape‐memory polymers (ESMPs) without affecting their shape‐memory performance is necessary to expand these polymers in practical applications. In this article, modified multi‐walled carbon nanotubes (MWCNTs) were prepared and used as efficient reinforcement for enhancing the comprehensive properties of ESMPs. Increases of nearly 289% to 444% for impact strength and 112% to 184% for tensile force were obtained by adding only 0.1 to 1 wt% epoxy‐modified MWCNTs. The addition of unmodified and carboxyl‐modified MWCNTs was also investigated but showed less impact on the mechanical properties of the ESMPs than epoxy‐modified MWCNTs. Thermogravimetry analysis (TGA) and dynamic mechanical analyses (DMA) showed that less than 1 wt% modified MWCNTs can enhance the heat resistance of ESMPs greatly. Although the shape recovery time for composite materials increased upon adding the MWCNTs, the entire recovery time was still less than 1 minute, and the shape recovery rate was relatively high, nearly 100%.