GpoSolver: a Matlab/C++ toolbox for global polynomial optimization

Global polynomial optimization can be a powerful tool when applied to engineering problems. One of the most successful methods for solving such problems is based on convex linear matrix inequality (LMI) relaxations. Software implementations of this approach can be found for example in Matlab toolboxes GloptiPoly and YALMIP. Matlab language makes it very easy when it comes to modelling polynomial problems. However, when using these toolboxes, Matlab is also required for the problem solving. GpoSolver aims at bridging this gap by providing a Matlab-based problem modelling toolbox supplemented by a problem-solving back end in a form of a C++ template library. Once a problem is conveniently modelled and parametrized in Matlab, a C++ class is automatically generated by GpoSolver. This class can be easily included into an existing codebase and used to solve different instances of the problem based on the supplied parameters.     

3D重构中的多项式约束模式*

针对基于单幅图像的3D重构因其约束条件的严重匮乏,而致使重构结果不确定的原因与机理进行了深入研究。以SFS重构方案为研究对象,提出首先将SFS问题规划为仅含二次约束的多项式系统,进而递次使用同伦分析法和精确线搜索技术,最后基于变量集构造一个SDP凸松弛。实验结果表明,这种重构方案不仅可以寻找所有全局解,优化迭代过程,加快收敛速度,而且可以避免产生不理想的局部解,彻底摆脱对初始假定的依赖,确保迭代过程收敛于一个全局极小值。借助多项式系统的完备解空间特性,大大提高了3D重构的精确度和唯一性,非常适用于非刚体表面重构。     

Molecular mobility in a homologous series of amorphous solid glucose oligomers

The molecular mobility of amorphous solid biomaterials influences the stability of dried foods and pharmaceuticals, the viability of seeds and spores, and the desiccation-tolerance of organisms during anhydrobiosis. Current understanding of how structure correlates with molecular mobility in the glassy state is inadequate. We used phosphorescence from vanillin dispersed in amorphous films to study the effect of temperature on molecular mobility in the homologous series of oligosaccharides glucose, maltose, maltotriose, maltotetraose, maltopentaose, maltohexaose, and maltoheptaose. Phosphorescence emission spectra and intensity decays were collected from −10 to as high as 130 °C. Emission peak energy, a measure of the extent of dipolar relaxation around the excited state prior to emission, decreased monotonically with temperature, decreasing more significantly in the glassy state in larger sugars (higher degree of polymerisation). The intensity decays were well fitted with sums of either four (glucose, maltose, maltotriose) or three exponentials (maltotetraose, maltopentaose, maltohexaose, maltoheptaose); fit lifetimes at each temperature varied over nearly two orders of magnitude, suggesting a comparable range in matrix dynamic heterogeneity. The lifetimes decreased monotonically with temperature, while the lifetime amplitudes favoured the long lifetime components at lower and short lifetime components at higher temperatures near T_g. Arrhenius analysis indicated that the rate of non-radiative decay, which reflects coupling of probe vibrations with matrix motions and thus provides an estimate of the matrix molecular mobility, increased with molecular size in the glassy state. Both apparent activation energy and activation entropy increased systematically with temperature in all sugars. These data provide additional evidence that the rate and extent of molecular mobility in glassy state carbohydrates is higher in sugars of greater molecular size (mass) and thus higher glass transition temperature and provides additional insight into the molecular dynamics of the glassy state in carbohydrates.     

随机需求下的选址-库存配送系统集成规划模型及算法

研究了随机需求条件下由单供应商、候选分拨中心和分销点构成的选址－库存问题, 分销点、分拨中心分别基于周期检查(R, s,Q)和连续检查(s, S)库存控制策略. 综合考虑库存成本、运输成本和设施成本之间的均衡关系, 建立了二级库存与无能力约束选址集成规划模型. 给出了适合求解实际规模问题的拉格朗日松弛算法, 提出了求解子问题的有效启发式方法, 改进了次梯度优化方法. 通过仿真试验验证了模型的正确性和算法的有效性. 最后讨论了相对于传统规划方法, 需求方差、服务水平、持有成本、提前期等关键库存控制参数对系统运营成本节约的影响规律.     

Time-varying discrete-time linear systems with bounded rates of variation: Stability analysis and control design

This paper investigates the problems of robust stability analysis and state feedback control design for discrete-time linear systems with time-varying parameters. It is assumed that the time-varying parameters lie inside a polytopic domain and have known bounds on their rate of variation. A convex model is proposed to represent the parameters and their variations as a polytope and linear matrix inequality relaxations that take into account the bounds on the rates of parameter variations are proposed. A feasible solution provides a parameter-dependent Lyapunov function with polynomial dependence on the parameters assuring the robust stability of this class of systems. Extensions to deal with robust control design as well as gain-scheduling by state feedback are also provided in terms of linear matrix inequalities. Numerical examples illustrate the results.     

Globally Optimal Estimates for Geometric Reconstruction Problems

We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality—or a combination of both—we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum.     

Dynamic mechanical and dielectric relaxations in poly(di-n-chloroalkylitaconates)

Dielectric and viscoelastic relaxation measurements have been carried out on poly(2-chloroethyl diitaconate) (PDCEI) and poly(3-chloropropyl diitaconate) (PDCPI) between 123 K and temperatures about 293 K above the glass transition temperatures.The two polymers exhibit three peaks, a γ-relaxation in the range from 133 to 193 K (at 1 Hz), a broad β-process, in the range from 193 to 293 K and a third peak observed in mechanical measurements at 323 K (PDCEI) and 293 K (PDCPI) probably corresponding to the α dynamic glass transition phenomena. In dielectric measurements, conductive contributions overlap the α-relaxation precluding the observation of peaks at temperatures above room temperature. The apparent activation energies for the γ-relaxation according to the mechanical and dielectric measurements are close to the values derived from the empirical force field molecular mechanics calculations. A comparison is made between the relaxational data of PDCEI and PDCPI by one hand and poly(di-n-propyl itaconate) (PDPI) and poly(di-n-butyl itaconate) (PDBI) by other. This comparison allows us to conclude the relevant role played by the chlorine atoms not only in the γ relaxations but also in the β relaxations of PDCEI and PDCPI.     

Dielectric investigation on poly(methylmethacrylate) films doped with p-nitroaniline

The dielectric behaviour of solution-grown thin films of poly(methylmethacrylate) containing p-nitroaniline (p-NA) as a dopant was investigated within the temperature range 60–90°C and a 20–10⁵ Hz frequency band. It is shown that these mixtures exhibit only one relaxation process similar to that of pure PMMA. However, the addition of p-NA increases both the height and the relaxation strength of the peaks and also shifts log f_m to higher frequencies. The additive causes narrowing of the loss curves and increases the activation energy for relaxation. These results are interpreted in terms of the hydrogen bonding effects of p-NA on localized motions of carboxymethyl dipoles in PMMA. An insight into the possible origins of the β- and α-relaxations in PMMA is also presented.     

Broadband dielectric spectroscopy of Nafion‐117, sulfonated polysulfone (sPSF) and sulfonated polyether ketone (sPEK) membranes

Nafion^®‐117, sulfonated polysulfone (sPSF) and sulfonated polyetherketone (sPEK) are characterized using broadband dielectric spectroscopy in the frequency range of 10 MHz–100 mHz. Overall, there are 4–5 relaxation processes in these sulfonated membranes and a comparison of their spectral features allows assigning the relaxation processes. At an optimum amplitude of ～100 mV_rms, all the relaxations are clearly defined as the electrode polarization is minimized. At low temperatures (?130 °C), these membranes show a broad relaxation peak in the mid‐frequency region, which quickly shifts towards the high‐frequency region as the temperature is increased to ?90 °C. This peak is observed in proton exchange membranes for the first time due to the use of low ac amplitude, and it is assigned to the relaxation of the confined water in the micro‐pores. With all the membranes, the peak associated with ? SO₃H group relaxation is observed in the same frequency range at a temperature of ～?80 °C. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134 , 44790.     

机会约束随机动态经济调度的凸松弛迭代求解法

大规模风电并网给电力系统运行带来了重大技术挑战,其出力的随机性和波动性增加了线路传输能力和备用调节能力不足的风险,传统的确定性经济调度方法已不完全适用。首先提出了一种基于混合高斯分布的机会约束随机动态经济调度模型,该模型将最小备用约束和线路传输容量约束建模为机会约束,并引入调频机组的仿射控制策略以实时平衡风功率的波动。然后提出了一种机会约束规划的松弛迭代求解方法,将随机调度模型转化为二次规划模型以实现快速有效求解。利用中国西南某省25个风电场的现场数据以及IEEE 118节点系统进行算例分析,验证了混合高斯分布对风电预测误差的拟合精度,以及所提方法的可行性。