On equivalent stability properties in semi-infinite optimization

This paper studies noncompact feasible sets of a semi-infinite optimization problem which are defined by finitely many equality constraints and infinitely many inequality constraints. The main result is the equivalence of the overall validity of the Extended Mangasarian Fromovitz Constraint Qualification with certain (topological) stability conditions. Furthermore, two perturbation theorems being of independent interest are presented.This work was supported by the Deutsche Forschungsgemeinschaft under grant Gu 304/1-2.     

非线性互补问题的一种不可行非内点连续方法

基于 Chen- Mangasarian光滑函数的一个子类 ,针对单调非线性互补问题给出了一种不可行非内点连续方法预估校正算法 ,并在适当的条件下 ,证明了算法具有全局线性收敛性和局部二次收敛性。     

Higher‐order generalized invexity in variational problems

We introduce higher‐order duality (Mangasarian type and Mond–Wier type) of variational problems. Under higher‐order generalized invexity assumptions on functions that compose the primal problem, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for this pair of problems. Also, we establish many examples and counter‐examples to support our investigation. Copyright © 2012 John Wiley & Sons, Ltd.     

Banach空间中多目标规划的局部有效解的必要条件

本文对Ｂａｎａｃｈ 空间中的多目标规划的局部有效解提出Ｆｒｉｔｚ Ｊｏｈｎ 必要条件和Ｋｕｈｎ－Ｔｕｃｋｅｒ必要条件,并且证明了多目标规划的Ｌａｇｒａｎｇｅ 正则性等价于一个标量规划问题的Ｌａｇｒａｎｇｅ 正则性．