Two fundamental convergence theorems for nonlinear conjugate gradient methods and their applications

1. IntroductionWe consider the global convergence of conjugate gradient methods for the unconstrainednonlinear optimization problemadn f(x),where f: Re - RI is continuously dtherelltiable and its gradiellt is denoted by g. Weconsider only the cajse where the methods are implemented without regular restarts. Theiterative formula is given byXk 1 = Xk Akdk, (1'1).and the seaxch direction da is defined bywhere gb is a scalar, ^k is a stenlength, and gb denotes g(xk).The best-known formulas fo…     

A Smoothing Newton-Type Algorithm of Stronger Convergence for the Quadratically Constrained Convex Quadratic Programming

In this paper we propose a smoothing Newton-type algorithm for the problem of minimizing a convex quadratic function subject to finitely many convex quadratic inequality constraints. The algorithm is shown to converge globally and possess stronger local superlinear convergence. Preliminary numerical results are also reported. Mathematics Subject Classification (1991): 90C33, 65K10 This author’s work was also partially supported by the Scientific Research Foundation of Tianjin University for the Returned Overseas Chinese Scholars and the Scientific Research Foundation of Liu Hui Center for Applied Mathematics, Nankai University-Tianjin University.     

Nd:YAG晶体板条低透射波前误差加工技术

针对高平均功率固体激光器对Nd:YAG晶体板条的技术需求,进行了Nd:YAG晶体板条低透射波前误差加工技术研究。详细分析了光学加工过程中引起板条端面透射波前畸变的误差来源,并提出工艺技术解决方案。实验结果表明,在板条抛光阶段通过采用合成盘硬抛光工艺以及新的工件装夹技术,能够解决传统板条加工工艺在面形及楔角精度方面可控性差的问题,更容易实现Nd:YAG晶体板条的低透射波前误差加工。对于150 mm30 mm2.5 mm规格的Nd:YAG晶体板条元件,端面透射波前畸变PV值达到0.74。     

光学元件中高频PSD2误差的实验研究

光学元件的中高频误差一般采用功率谱密度（PSD）表示,其划分为PSD1和PSD2两个频段。针对目前国内外研究较少的PSD2频段误差,分析和实验研究了其潜在的影响因素。采用沥青和聚氨酯盘抛光熔石英元件的实验结果显示：小工具数控相比传统全口径抛光并未增大PSD2误差,而抛光盘材质对PSD2误差具有决定性的影响。沥青盘在抑制PSD2误差方向具有较好的优越性,工件表面的PSD2指标能够满足要求,而聚氨酯抛光元件表面的PSD2误差则较高。针对这一问题,提出采用固结金刚石丸片修整聚氨酯垫,通过细化金刚石颗粒获得了合格的PSD2指标。     

组氨酸(His)与钴(Ⅱ)相互作用的热力学摩尔吸光系数的研究

测出钴（Ⅱ）与组氨酸的紫外可见吸收光谱和配合反应的热力学摩尔吸光系数,比较Ｃｏ（Ⅱ）与组氨酸形成不同组成的配合物的稳定性。     

接枝共聚改性氧化淀粉及电流变性研究

通过自由基接枝共聚的方法，合成了改性的氧化淀粉-BA—MAA—Gd共聚物，采用红外光谱、扫描电镜、同步热分析、x射线粉末衍射等方法对产物进行了结构表征。用接枝物制备了电流变液，测定了在不同接枝物含量和电场强度下体系的电流变效应。实验结果表明：该电流变液体系的剪切应力随着电场强度的增大而增大；而在相同电场强度下，剪切应力则随电流变液中接枝物含量的增加而增大。     

Study on the reaction kinetics between PBT and epoxy by a novel rheological method

In the present study, the reaction kinetics of polybutylene terephthalate (PBT) and epoxy system was studied by a novel rheological method. The reaction process was determined by rheological test and the results showed that there were three stages in the reaction between PBT and epoxy, which were reaction-controlling stage (stage I), reaction-stagnation stage (stage II) and diffusion-controlling stage (stage III). In addition, the stage I was selected to study the reaction kinetics by the rheological method. The results showed that the reaction between PBT and epoxy could be classified as a pseudo-first-order reaction due to the excessive amount of epoxy group. Furthermore, the reaction apparent activation energy of the stage I determined by the rheological method was 143 kJ/mol. To confirm these results, the reaction kinetics was also evaluated by the endgroup determination method, and the results showed that the reaction could also be classified as a pseudo-first-order reaction. Moreover, the apparent activation energy of the reaction was 116 kJ/mol, which was similar to that of the value obtained by the rheological method.     

An introduction to a class of matrix cone programming

In this paper, we define a class of linear conic programming (which we call matrix cone programming or MCP) involving the epigraphs of five commonly used matrix norms and the well studied symmetric cone. MCP has recently been found to have many important applications, for example, in nuclear norm relaxations of affine rank minimization problems. In order to make the defined MCP tractable and meaningful, we must first understand the structure of these epigraphs. So far, only the epigraph of the Frobenius matrix norm, which can be regarded as a second order cone, has been well studied. Here, we take an initial step to study several important properties, including its closed form solution, calm Bouligand-differentiability and strong semismoothness, of the metric projection operator over the epigraph of the $l_1,\,l_\infty $ , spectral or operator, and nuclear matrix norm, respectively. These properties make it possible to apply augmented Lagrangian methods, which have recently received a great deal of interests due to their high efficiency in solving large scale semidefinite programming, to this class of MCP problems. The work done in this paper is far from comprehensive. Rather it is intended as a starting point to call for more insightful research on MCP so that it can serve as a basic tool to solve more challenging convex matrix optimization problems in years to come.     

Effects of calcium ions on solubility and aggregation behavior of an anionic sulfonate gemini surfactant in aqueous solutions

In this work, a ternary composite, Pt/TiO(2)/RGO (reduced graphite oxide), was prepared via immobilizing Pt particles onto the TiO(2)/RGO composite that was obtained via redox reaction of TiCl(3) and GO. The composite was characterized by different techniques including X-ray diffraction, transmission electron microscopy, and X-ray photoelectron spectroscopy. The TiO(2) particles with size less than 10 nm were uniformly distributed throughout the RGO, and almost each Pt particle with size around 3 nm adhered to TiO(2) particles, resulting in high dispersion of all Pt particles on the support. The Pt particles were in the electron-deficient state due to the strong interactions with the TiO(2) particles and the RGO support. The catalytic performance of the composite for nitrobenzene hydrogenation was investigated under solvent-free condition. It was indicated that the Pt/TiO(2)/RGO catalyst exhibited high activity with a turnover frequency (e.g., 59,000 h(-1)) as well as superior selectivity to aniline (e.g., >99%). Moreover, the catalyst can be reused for six times without any activity loss, which resulted from the stable structure of the catalyst.     

Structural Transformation of Methoxy‐Substituted Benzo[de]benzo[4,5]imidazo[2,1‐a]isoquinolin‐7‐ones

Structural transformation of two methoxy derivatives of benzo[de]benzo[4,5]imidazo[2,1‐a]‐isoquinolin‐7‐one were determined via spectroscopic analysis. The transformation mechanism was proposed as the breakage and reformation of the lactam bond.