A globally convergent Newton method for solving strongly monotone variational inequalities

Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.     

关于多正解问题的某些研究

本文以ｆｐ 同伦方法为工具，借助于一些适当的变换，研究有序的（Ｂ）空间中的集值映象方程的多正解问题；在文中的有关工作中，还使用了集值映象的拟导数的某些性质．     

Research on sound radiation from body in free field

I.IntroductionWhenastructurcvibratcs,itsvibratingsurfacewillmakesurroundingmediummovetogethcrwithit.Ifthernotionissofastthatthcmediumroundthestructureproduccaloca1contractionandcxpansionandthcypropagatefaraway,thesoundradiationisformed.Itispossiblctodcscribeanalytica11ytheradiationfic1dofsimplyandregularlyshapcdsourcessuchaspointsoundsourccs,spherica1soundsourccsandinflnite1engthllnearsoundsourccs,butitisa1mostimpossib1ctosolvetheradiationfiledbyanyanalyt-ica1methodforsourcesofvcrycomplicateds…     

软X光辐射烧蚀实验方法研究

 用强激光辐照金箔靶，以金箔背侧软X光辐射为基础，提出了软X光辐射烧蚀研究的新靶型、新方法，做了C₈H₈样品辐射烧蚀初步实验。     

Extended convergence results for the method of multipliers for nonstrictly binding inequality constraints

In this paper, we extend the classical convergence and rate of convergence results for the method of multipliers for equality constrained problems to general inequality constrained problems, without assuming the strict complementarity hypothesis at the local optimal solution. Instead, we consider an alternative second-order sufficient condition for a strict local minimum, which coincides with the standard one in the case of strict complementary slackness. As a consequence, new stopping rules are derived in order to guarantee a local linear rate of convergence for the method, even if the current Lagrangian is only asymptotically minimized in this more general setting. These extended results allow us to broaden the scope of applicability of the method of multipliers, in order to cover all those problems admitting loosely binding constraints at some optimal solution. This fact is not meaningless, since in practice this kind of problem seems to be more the rule rather than the exception.In proving the different results, we follow the classical primaldual approach to the method of multipliers, considering the approximate minimizers for the original augmented Lagrangian as the exact solutions for some adequate approximate augmented Lagrangian. In particular, we prove a general uniform continuity property concerning both their primal and their dual optimal solution set maps, a property that could be useful beyond the scope of this paper. This approach leads to very simple proofs of the preliminary results and to a straight-forward proof of the main results.The author gratefully acknowledges the referees for their helpful comments and remarks. This research was supported by FONDECYT (Fondo Nacional de Desarrollo Científico y Technológico de Chile).     

平面分层介质结构全波分析综述

本文综述了广义谱域导抗法，直线法及直线法的快速算法，全波离散镜象法等主要方法，并对各种方法的特点进行了比较，这些方法可有效地处理平面分层介质结构问题，文中包括作者近期的研究成果。     

β—BBO晶体的电光性能

用干涉法测量了β－ＢＢＯ晶体的电光系数：γ２２＝２．６，γ３３＝０．２３，γ３１＝０．２５，γ５１＝－３．５×１０－１２ｍ／Ｖ。结果表明如果在Ｙ方向加电场，Ｚ方向通光，β—ＢＢＯ晶体可能制作成有应用价值的光开关。     

非线性网络的混合域分析法

本文研究了对非线性网络进行混合域分析的谐波平衡法,它既可以改善计算精度,又可以提高速度,计算速度比全时域分析提高十倍以上,并且比全频域法要简单得多.它可以用来分析混频器、功率上变频器、振荡器等非线性电路.     

高阶半线性抛物型方程组的生命跨度

其中m,P,q>1．利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度 [0,T)给出估计．     

On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.