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).     

Optimal algebraic multilevel preconditioning for local refinement along a line

The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.     

三系数有限元向量尺度函数的构造

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.     

广义分解定理与两个不等式

本文给出了Banach空间广义分解定理的一个初等证明,并利用它来证明两个对称不等式.这是首次在Banach空间获得这样的不等式.     

抓好数学建模竞赛 推动数学教学改革

本文通过近几年组织数学建模教学和指导学生参加竞赛的实践 ,探索抓好数学建模竞赛 ,促进数学教学改革 ,推动数学素质教育 ,提高人才培养质量的途径、措施和方法     

牛顿弦截法预估校正迭代格式的收敛阶

研究如下形式的牛顿弦截法的预估校正(P.C.)格式:P(预估):~xk+1=xk-(xk-xk-1)f(xk)f(xk)-f(xk-1)C(校正):xk+1=xk-(~xk+1-xk)f(xk)f~(xk+1)-f(xk)证明了它的收敛阶为2.618.     

Little higgs models and T parity

Little Higgs models are an interesting extension of the Standard Model at the TeV scale. They provide a simple and attractive mechanism of electroweak symmetry breaking. We review one of the simplest models of this class, the Littlest Higgs model, and its extension with T parity. The model with T parity satisfies precision electroweak constraints without fine-tuning, contains an attractive dark matter candidate, and leads to interesting phenomenology at the Large Hadron Collider (LHC).     

相位差与q变形广义相干叠加态的压缩特性

对于q变形的非简谐振子广义相干态的叠加态β〉+eiφβeiδ〉,其量子涨落的可能高阶压缩阶数可以表示为k≠2πn/δ,这里n是整数.当δ=π时,压缩阶数不能是偶数即只能是奇数,这正是q变形非简谐振子广义奇偶相干态的结果.由此表明参数相位差δ对决定q变形的非简谐振子广义相干态叠加态的高阶压缩阶数起决定性作用.     

The Properties of Light Pressure Force with High Order in Laser Fields

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｂｏｔｈｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎｄｅｘｐｅｒｉｍｅｎｔａｌｉｎｖｅｓｔｉｇａｔｉｏｎｓｏｎｌａｓｅｒｃｏｏｌｉｎｇａｎｄｔｒａｐｐｉｎｇｈａｖｅｂｅｃｏｍｅｏｎｅｏｆｔｈｅｍａｊｏｒｆｉｅｌｄｓｉｎａｔｏｍｉｃ,ｍｏｌｅｃｕｌａｒａｎｄｏｐｔｉｃａｌ ｐｈｙｓｉｃｓ[1～ 8] .Ｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｌａｓｅｒｃｏｏｌｉｎｇａｎｄｔｒａｐｐｉｎｇｔｅｃｈｎｏｌｏｇｙｉｓｉｍｐｏｒｔａｎｔｆｏｒｔｈｅａｐｐｌｉｃａｔｉｏｎｓｓｕ…     

Lorentz-Compton佯谬与一个双赢判决性散射实验设计

通过对“可见光区域是否存在Compton效应”的讨论而进一步深化到经典条件下“光的量子理论能否包含光的经典电磁理论”的实验验证,发现了Lorentz-Compton佯谬,并基于逆Compton散射设计了一个敏感而又可行的双赢判决性散射实验来解决此佯谬。