A Theorem of the Alternative and Its Application to the Optimization of Set-Valued Maps

In this paper, we establish a theorem of the alternative in ordered linear topological spaces. Then, optimality conditions for the optimization of set-valued maps are obtained.  

基于变参数模型的中国能源消费经济增长关系研究

本文利用1953—2002年的统计数据和状态空间模型对中国能源消费与经济增长关系进行了研究。我们的结论是:(1)中国能源消费与经济增长之间存在一种随时间不断变化的长期均衡关系即变参数协整关系;(2)基于状态空间模型的变参数估计很好地揭示了中国能源消费弹性的时变规律。  

复正定矩阵的Minkowski不等式

建立了复正定矩阵的几个行列式不等式，将正定Ｈｅｒｍｉｔｅ阵的Ｍｉｎｋｏｗｓｋｉ不等式、 Ｏｓｔｒｏｗｓｋｉ－Ｔａｕｓｓｋｙ不等式推广到了复正定矩阵上，推广改进了一些文献的结果．  

线性拓扑空间中向量极值问题的广义 Kuhn-Tucker 条件

文[1]对 n 维欧氏空间 R~n,建立了在次似凸(Subconvexlike)映射下的择一定理,并以此证明具有弱凸性的极大极小定理.本文将择一定理推广到序线性拓扑空间,从而得出向量极值问题的广义 Kuhn-Tucker 条件和 Lagrange 乘子存在定理.  

Theorems of the Alternative and Optimization with Set-Valued Maps

In this paper, the concept of generalized cone subconvexlike set-valued mapsis presented and a theorem of alternative for the system of generalizedinequality–equality set-valued maps is established. By applying thetheorem of the alternative and other results, necessary and sufficientoptimality conditions for vector optimization problems with generalizedcone subconvexlike set-valued maps are obtained.  

Three kinds of generalized convexity

This paper gives some properties of quasiconvex, strictly quasiconvex, and strongly quasiconvex functions. Relationships between them are discussed.This research was supported in part by the National Natural Science Foundation of China. The author would like to thank Professor M. Avriel for valuable comments about this paper.  

线性拓扑空间中向量极值问题的广义 Kuhn-Tucker 条件

文[1]对 n 维欧氏空间 R~n,建立了在次似凸(Subconvexlike)映射下的择一定理,并以此证明具有弱凸性的极大极小定理.本文将择一定理推广到序线性拓扑空间,从而得出向量极值问题的广义 Kuhn-Tucker 条件和 Lagrange 乘子存在定理.  

On E-Convex Sets, E-Convex Functions, and E-Convex Programming

Recently, E-convex sets and E-convex functions were introduced in Ref. 1. However, some results seem to be incorrect. In this note, some counterexamples are given.  

定常Stokes问题的边界积分方程法

1.前言 定常Stokes问题本身虽然只反映在小雷诺数情况下不可压缩粘性流体的定常流动,然而却为处理完整的Navier-Stokes方程奠定了基础. Stokes问题一般有两种公式化途径,一是通过流函数,二是利用速度-压力公式.两种公式化途径的区域类型数值方法,如有限差分法及有限单元法,已有不少工作,见[3]和[11].近年来,对这两种公式化途径的边界类型数值方法的研究,也获得一些结果.