【作者】 闻珏莹；

【导师】 夏尊铨；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2005， 硕士

【摘要】 本文首先给出了混合约束条件下拟可微函数的Fritz John条件,其次推出了关于K-凸化集性质的三个定理,最后基于Fejer映射的基本原理,构造出了一类非光滑半无限规划问题的Fejer算法并证明其收敛性。 第2章在Polyakova正则和Shapiro正则的定义下,给出了混合约束条件下的拟可微函数的Fritz John条件。 第3章首先给出了两种凸化集的定义。针对Jeyakumar和Luc凸化集,定义了正则凸化集,构造了唯一极小正则凸化集和极小凸化集,并给出了凸化集的极值条件。最后,给出了一般Banach空间算子的K-凸化集的基本定义,推出了关于算子K-凸化集性质的三个定理。 第4章首先给出了Fejer映射的基本性质,然后基于Fejer映射的基本原理给出了一类非光滑半无限规划问题的Fejer算法并证明其收敛性。更多还原

【Abstract】 Firstly, Fritz John conditions for quasi-differentiable functiongs with hybrid constraints are proposed in this paper. Sencondly, three theorems on properties of K’-convexificator of operator are presented. Lastly, based on basic principle of Fejer mapping, we construct Fejer Algorithm for solving a class of nonsmooth semi-infinite programming problems and prove its convergence.In Chapter 2, Fritz John conditions for quasi-differentiable functions with hybrid constraints are presented from the definitions of Polyakova regularity and Shapiro regularity.In Chapter 3,we first introduce two definitions of convexificator. Contraposing Jeyaku-mar and Luc convexificators,we define a regular convexificator. Then we construct unique minimum regular convexificator and minimum convexificator , moreover,some conditions for convexificator are given. At the last of the chapter, the basic definition of K’-convexificator of operator in general Banach space is investigated, and three theorems on properties of K’-covexificatoe of operator are presented.In Chaper 4,we first give some fundamental properties of Fejer mapping. And the based on the fundamental principle of Fejer mapping, Fejer Algorithm for solving a clars of nonsmooth semi-infinite programming problems is presented and prove its convergence.更多还原