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| 约束优化问题中常用的约束规范及其相互关系 | |
| 引用本文： | 张序萍,王永丽,贺国平. 约束优化问题中常用的约束规范及其相互关系[J]. 数学的实践与认识, 2006, 36(1): 181-189 |
| 作者姓名： | 张序萍 王永丽 贺国平 |
| 作者单位： | 1. 山东科技大学信息科学与工程学院,山东,青岛,266510;山东科技大学泰安校区公共课部,山东,泰安,271000 2. 山东科技大学信息科学与工程学院,山东,青岛,266510;上海交通大学数学系,上海,200240 3. 山东科技大学信息科学与工程学院,山东,青岛,266510 |
| 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. |
| 关 键 词： | 约束优化问题 约束规范 拉格朗日乘子 |
| 修稿时间： | 2004-10-15 |
The Relationship Among Various Constraint Qualifications in Nonlinear Constrained Optimization |
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| ZHANG Xu-ping,WANG Yong-li,HE Guo-ping. The Relationship Among Various Constraint Qualifications in Nonlinear Constrained Optimization[J]. Mathematics in Practice and Theory, 2006, 36(1): 181-189 | |
| Authors: | ZHANG Xu-ping WANG Yong-li HE Guo-ping |
| Abstract: | 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. |
| Keywords: | constrained optimization problem constraint qualification lagrange multiplier |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |