自反Banach空间中向量优化问题弱有效解集特性的进一步研究  

Further Study on the Nonemptiness and Boundedness of the Weakly Efficient Solution Set of a Convex Vector Real Reflexive Banach Space with Application

作　　者：张亚琴[1] 

机构地区：[1]河北交通职业技术学院土木工程系,石家庄050091

出　　处：《应用数学学报》2011年第1期102-112,共11页Acta Mathematicae Applicatae Sinica

摘　　要：本文分别研究了在无限维自反Banach空间中,当控制结构为多面体锥时,一般凸向量优化问题和锥约束凸向量优化问题的弱有效解集的非空有界性,并且把结论应用到了一类罚函数方法的收敛性分析上.In this paper,I first characterize the nonemptiness and boundedness of the weakly efficient solution set of convex vector optimization problem,especially a cone-constrained convex vector optimization problem in infinite-dimensional real reflexive Banach spaces. More specifically,I will consider the covex vector optimization problem when the objective space R^m is ordered by a nontrivial,polyhedral cone with nonempty interior instead of the nonnegative orthant R_＋~m.Then,I apply the characterizations to the convergence analysis of a class of penalty methods.

关 键 词：多面体锥 弱有效解 正极锥 锥约束优化 罚方法 

分 类 号：O221.6[理学—运筹学与控制论]