Decomposition Methods for Differentiable Optimization Problems over Cartesian Product Sets

This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approx imation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms.     

具有奇异值分解性质的代数

设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.     

On the spectra of finite-dimensional quadratic Bose operators

A complete study of the spectrum of a finite-dimensional Bose operator is carried out in the paper. The cases in which the spectrum is discrete or continuous are studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 835–854, June, 1997. Translated by A. M. Chebotarev     

Banach空间上的框架与Riesz基

本文讨论Banach空间上框架、无冗框架与Riesz基之间的关系及它们的稳定性．     

双线性系统的无反馈解耦线性化

用现代微分几何方法研究了双线性控制系统的解耦线性化问题，给出了一般双线性系统解耦线性化的充分条件及严格双线性系统解耦线性化的充要条件，并举例说明了本文的结论。     

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.     

A generic view of Dantzig-Wolfe decomposition in mixed integer programming

The Dantzig-Wolfe reformulation principle is presented based on the concept of generating sets. The use of generating sets allows for an easy extension to mixed integer programming. Moreover, it provides a unifying framework for viewing various column generation practices, such as relaxing or tightening the column generation subproblem and introducing stabilization techniques.     

A note on continuously decomposed evolving exchange economies

It is routine to demonstrate in the exchange economy framework that small changes of individual preferences and endowments always result in small changes of the derived excess demand functions as one should expect. Though being as desirable for reasons of the consistency of the whole approach, however, a precise proof of the converse direction so far is still open to question. The present paper shows that it is actually true. We use a decomposition method for aggregate excess demand functions developed by Mas-Colell which is derived from the well-known decomposition method developed by Sonnenschein and perfected by Debreu and Mantel. Our result fills in a notorious gap in the line of economic justification usually given for this decomposition, or disaggregation, method in that comparative static analysis would be restricted if the decomposition of excess demand functions would not be continuous.     

基于阿贝尔黑格斯变量的杨-米尔斯理论的红外阿贝尔化

通过SU(2)规范场的法捷耶夫-Niemi分解给出了有效阿贝尔-黑格斯型作用量的 一个计算方法. 具体指出了该分解中所用的自然规范固定以及阿贝尔投射与杨-米尔斯理论的红外动力学之间的内在关系. 推导出了色电场的一个伦敦型方程.     

Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices).