First-Order Algorithms for Generalized Semi-Infinite Min-Max Problems

We present a first-order algorithm for solving semi-infinite generalized min-max problems which consist of minimizing a function f⁰(x) = F(¹(x), .... , ^m (x)), where F is a smooth function and each ⁱ is the maximum of an infinite number of smooth functions.In Section 3.3 of [17] Polak finds a methodology for solving infinite dimensional problems by expanding them into an infinite sequence of consistent finite dimensional approximating problems, and then using a master algorithm that selects an appropriate subsequence of these problems and applies a number of iterations of a finite dimensional optimization algorithm to each of these problems, sequentially. Our algorithm was constructed within this framework; it calls an algorithm by Kiwiel as a subroutine. The number of iterations of the Kiwiel algorithm to be applied to the approximating problems is determined by a test that ensures that the overall scheme retains the rate of convergence of the Kiwiel algorithm.Under reasonable assumptions we show that all the accumulation points of sequences constructed by our algorithm are stationary, and, under an additional strong convexity assumption, that the Kiwiel algorithm converges at least linearly, and that our algorithm also converges at least linearly, with the same rate constant bounds as Kiwiel's.     

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.     

On NCP-Functions

In this paper we reformulate several NCP-functions for the nonlinear complementarity problem (NCP) from their merit function forms and study some important properties of these NCP-functions. We point out that some of these NCP-functions have all the nice properties investigated by Chen, Chen and Kanzow [2] for a modified Fischer-Burmeister function, while some other NCP-functions may lose one or several of these properties. We also provide a modified normal map and a smoothing technique to overcome the limitation of these NCP-functions. A numerical comparison for the behaviour of various NCP-functions is provided.     

概率论与数理统计实验教学案例设计

为克服传统数学教学模式局限于理论教学的弊端而倡导实践教学,设计出一个概率论与数理统计实验教学的案例,将线性回归分析应用于高光谱遥感图像的处理之中.     

A feasible semismooth asymptotically Newton method for mixed complementarity problems

 Semismooth Newton methods constitute a major research area for solving mixed complementarity problems (MCPs). Early research on semismooth Newton methods is mainly on infeasible methods. However, some MCPs are not well defined outside the feasible region or the equivalent unconstrained reformulations of other MCPs contain local minimizers outside the feasible region. As both these problems could make the corresponding infeasible methods fail, more recent attention is on feasible methods. In this paper we propose a new feasible semismooth method for MCPs, in which the search direction asymptotically converges to the Newton direction. The new method overcomes the possible non-convergence of the projected semismooth Newton method, which is widely used in various numerical implementations, by minimizing a one-dimensional quadratic convex problem prior to doing (curved) line searches. As with other semismooth Newton methods, the proposed method only solves one linear system of equations at each iteration. The sparsity of the Jacobian of the reformulated system can be exploited, often reducing the size of the system that must be solved. The reason for this is that the projection onto the feasible set increases the likelihood of components of iterates being active. The global and superlinear/quadratic convergence of the proposed method is proved under mild conditions. Numerical results are reported on all problems from the MCPLIB collection [8]. Received: December 1999 / Accepted: March 2002 Published online: September 5, 2002 RID="★" ID="★" This work was supported in part by the Australian Research Council. Key Words. mixed complementarity problems – semismooth equations – projected Newton method – convergence AMS subject classifications. 90C33, 90C30, 65H10     

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…     

Mild and Efficient Deoxygenation of Sulfoxides to Sulfides Using HfCl4/KBH4 System

HfCl₄/KBH₄ was found to be a facile, efficient, convenient, and chemoselective system for the deoxygenation of dialkyl, diaryl, and aryl alkyl sulfoxides, especially for the reduction of dibenzyl sulfoxide to the corresponding sulfides under mild conditions. In addition, the HfCl₄/KBH₄ system could be used in reduction of some other sulfur-bearing substrates to the corresponding sulfides, such as 2,2′-dibenzothiazolyl disulfide, but this reducing system could not reduce sulfolane, diphenyl sulfone, p-toluenesulfonic acid, and p-toluenesulfonyl chloride to their corresponding thiophenols.     

宁镇地区燕山期矽卡岩矿床成矿系统稀土元素地球化学研究

通过宁镇地区燕山期矽卡岩矿床成矿系统的稀土元素特征研究,了解了矽卡岩矿床成矿系统的稀土元素地球化学演化规律特征及其制约机制,为矽卡岩型多金属矿床成矿规律及成矿预测研究提供新的地质地球化学信息依据。研究表明,矽卡岩矿床成矿系统稀土演化规律为:矽卡岩期,干矽卡岩阶段到湿矽卡岩阶段稀土组分含量增加;矽卡岩期晚期到热液期早期降低;热液期,汽成热液氧化物阶段到高中温硫化物阶段增加,到中低温硫化物阶段降低。演化规律主要是受自身富集稀土元素的强度、流体含矿性、运移分配及成矿的物理化学条件的影响。矽卡岩矿床成矿系统主要矽卡岩化的发育及其分带性所具有成矿专属性等特点,都为进一步寻找矽卡岩型多金属矿床提供新的地质地球化学信息。     

A design concept of long-wavelength fluorescent analogs of rhodamine dyes: replacement of oxygen with silicon atom

Replacement of the oxygen with a silicon atom on the rhodamine framework produces a strong red-emission fluorophore which has a high molar extinction coefficient and 90 nm red shift relative to rhodamine dye PY.     

Kinetics study on melt compounding of carbon nanotube/polypropylene nanocomposites

The multiwalled carbon nanotubes/polypropylene nanocomposites (PP/CNTs) were prepared by melt mixing using maleic anhydride grafted polypropylene (mPP) as the compatibilizer. The effect of mPP on dispersion of CNTs was then studied using the tool of rheology, aiming at relating the viscoelastic behaviors to the mesoscopic structure of CNTs. To further explore the kinetics of hybrid formation, a multilayered sample with alternatively superposed neat mPP and binary PP/CNTs microcomposites (without addition of mPP) sheets was prepared and experienced dynamic annealing in the small amplitude oscillatory shear flow. The results show that melt blending CNTs with PP can only yield the composites with microscale dispersion of CNTs, while adding mPP promotes nanoscale dispersion of CNTs as smaller bundles or even as individual nanotubes, reducing percolation threshold as a result. However, the values of apparent diffusivities of the composites are in same order with that of self‐diffusion coefficients of the neat PP, indicating that the presence of detached CNTs nearly does not inhibit PP chain motion. Hence, the activation energy of hybrid formation is close to the self‐diffusion of PP. This also indicates that although addition of mPP can improve the compatibility between CNTs and PP thermodynamically, those dynamic factors, such as shear flow, however, may be the dominant role on hybrid formation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 608–618, 2009