约束优化问题中常用的约束规范及其相互关系  

The Relationship Among Various Constraint Qualifications in Nonlinear Constrained Optimization

作　　者：张序萍[1] 王永丽[1] 贺国平[1] 

机构地区：[1]山东科技大学信息科学与工程学院

出　　处：《数学的实践与认识》2006年第1期181-189,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金资助项目(10171055)

摘　　要：详细分析了约束优化问题中几种常见的约束规范,如L ICQ,SM FCQ,M FCQ,CRCQ,CPLD以及伪正规,拟正规和拟正则约束规范.针对等式和不等式约束问题讨论了它们与拉格朗日乘子的存在性及其性质之间的关系,给出了各种约束规范之间的关系图.特别通过反例,说明了WM FCQ在含等式约束的问题中不是一种约束规范.We analyze several Constraint Qualifications in constrained optimization in detail, such as LICQ, SMFCQ, MFCQ, CRCQ, CPLD, Pseudonormality, Quasinormality and Quasiregularity Constraint Qualification. Their definitions are listed and the property of lagrange multipliers under these Constraint Qualifications are discussed for equality and inequality constrained optimization. The relationship between all these Constraint Qualifications are concluded and a relation graph is given. Moreover, we also show that the ＂WMFCQ＂ condition is not a Constraint Qualification by a counterexample.

关 键 词：约束优化问题 约束规范 拉格朗日乘子 不等式约束 CPLD 拟正规 拟正则 关系图 反例 

分 类 号：O224[理学—运筹学与控制论]