Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.     

Impact of Partial Separability on Large-Scale Optimization

ELSO is an environment for the solution oflarge-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partialseparability structure of the function to computethe gradient efficiently using automatic differentiation.We demonstrate ELSO's efficiency by comparing thevarious options available in ELSO.Our conclusion is that the hybrid option in ELSOprovides performance comparable to the hand-coded option, while having the significantadvantage of not requiring a hand-coded gradient orthe sparsity pattern of the partially separable function.In our test problems, which have carefully coded gradients,the computing time for the hybrid AD option is within a factor of two of thehand-coded option.     

一类It型非线性时滞关联随机大系统的分散鲁棒控制

在非线性项满足全局Lipschitz条件下,本文研究了一类It型非线性时滞关联随机大系统的分散鲁棒控制问题.系统的时滞是关于状态和控制输入的.基于Lyapunov泛函及线性矩阵不等式(LMI)的分析方法,得到了无记忆状态反馈控制器使整个时滞关联随机大系统可镇定的充分条件.     

一类拟线性大系统的稳定性

本文应用大系统的分解方法和一个推广的不等式,研究了一类拟线性大系统的稳定性问题,所得结果简洁、易于验证,且推导过程不复杂,最后给出了应用实例。     

大规模界约束优化的子空间截断牛顿法

给出了大规模界约束优化的一个子空间截断牛顿法。利用截断牛顿法修正非有效约束所对应的变量，用投影梯度法修正有效约束所对应的变量，文中证明了方法的整体收敛性，并对方法进行了数值试验，且与子空间有限内存拟牛顿法进行了数值比较。     

On the generality of a cosmological speculation based on Heisenberg's principle

In a previous work [Hernández-Bermejo, B. (1996) Heisenberg's principle: A cosmological speculation, Speculations in Science and Technology, 19, 253], it was speculated that the lack of homogeneity of the large-scale structure of the universe may be due to quantum fluctuations of space in the early universe. This was argued for a Friedmann-type universe for which both the curvature and the cosmological constant were zero. Here it is shown that the same considerations are valid for arbitrary values of the curvature and .     

Two optimal Dai–Liao conjugate gradient methods

Two adaptive choices for the parameter of Dai–Liao conjugate gradient (CG) method are suggested. One of which is obtained by minimizing the distance between search directions of Dai–Liao method and a three-term CG method proposed by Zhang et al. and the other one is obtained by minimizing Frobenius condition number of the search direction matrix. Global convergence analyses are made briefly. Numerical results are reported; they demonstrate effectiveness of the suggested adaptive choices.     

Cost-Effective and Large-Scale Synthesis of 16:0 Lysophosphatidic Acid

Abstract

Lysophosphatidic acid (LPA) is a bioactive compound that has gained attention because of its role in neoplastic diseases. Popularity of the compound has necessitated the use of large quantities of the phospholipid for in vivo and in vitro testing, but methods for generating LPA require the use of costly procedures, namely phosphoramidite coupling reagents. Additionally there has been no reported large-scale synthesis of LPA. In the present study we report the cost-effective and large-scale synthesis of 16:0 LPA.     

Mathematical modeling of a slurry reactor for DME direct synthesis from syngas

In this paper,an axial dispersion mathematical model is developed to simulate a three-phase slurry bubble column reactor for direct synthesis of dimethyl ether(DME) from syngas.This large-scale reactor is modeled using mass and energy balances,catalyst sedimentation andsingle-bubble as well as two-bubbles class flow hydrodynamics.A comparison between the two hydrodynamic models through pilot plantexperimental data from the literature shows that heterogeneous two-bubbles flow model is in better agreement with the experimental data thanhomogeneous single-bubble gas flow model.Also,by investigating the heterogeneous gas flow and axial dispersion model for small bubblesas well as the large bubbles and slurry(i.e.including paraffins and the catalyst) phase,the temperature profile along the reactor is obtained.Acomparison between isothermal and non-isothermal reactors reveals no obvious performance difference between them.The optimum values ofreactor diameter and height were obtained at 7 m and 50 m,respectively.The effects of operating variables on the axial catalyst distribution,DME productivity and CO conversion are also investigated in this research.     

基于飞秒激光模间拍频法的大尺寸测距方法

本文基于飞秒激光模间拍频法实现多波长相位式绝对距离测量, 通过改变光频梳重复频率合成波长扩大测距量程, 并采用监测臂和双快门切换系统补偿和消除由电路产生的相位差单向漂移和大幅抖动. 实验中以20倍重复频率的拍频进行测量, 在30 min内相位测量的标准偏差为0.022°; 与双频激光干涉仪比对1125 mm行程内位移测量结果, 测距精度优于50 μm; 实验验证了合成波长方法扩大量程方案的可行性, 获得的测距重复性优于3 μm, 该系统理论上可扩展量程至7.5 km.