| 均衡约束数学规划问题的一种新的约束规格 |
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| 引用本文： | 童毅,吴国民,赵小科. 均衡约束数学规划问题的一种新的约束规格[J]. 数学杂志, 2017, 37(2): 376-382 |
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| 作者姓名： | 童毅 吴国民 赵小科 |
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| 作者单位： | 武汉大学数学与统计学院, 湖北 武汉 430072,北京石油化工学院数理系, 北京 102617,武汉大学数学与统计学院, 湖北 武汉 430072 |
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| 基金项目： | 国家自然科学基金资助（71471140）. |
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| 摘 要： | 本文研究了均衡约束数学规划(MPEC)问题.利用其弱稳定点,获得了一种新的约束规格–MPEC的伪正规约束规格.用一种简单的方式,证明了该约束规格是介于MPEC-MFCQ(即MPEC,Mangasarian-Fromowitz约束规格)与MPEC-ACQ(即MPEC,Abadie约束规格)之间的约束规格,因此该约束规格也可以导出MPEC问题的M-稳定点.最后通过两个例子,说明了该约束规格与MPEC-MFCQ以及与MPEC-ACQ之间是严格的强弱关系.
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| 关 键 词： | 约束规格 伪正规 均衡约束数学规划 稳定点 |
| 收稿时间： | 2014-11-10 |
| 修稿时间： | 2015-05-06 |
A NEW CONSTRAINT QUALIFICATION FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS |
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| TONG Yi,WU Guo-min and ZHAO Xiao-ke. A NEW CONSTRAINT QUALIFICATION FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS[J]. Journal of Mathematics, 2017, 37(2): 376-382 |
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| Authors: | TONG Yi WU Guo-min ZHAO Xiao-ke |
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| Affiliation: | School of Mathematics and Statistics, WuHan University, Wuhan 430072, China,Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China and School of Mathematics and Statistics, WuHan University, Wuhan 430072, China |
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| Abstract: | This paper considers mathematical programs with equilibrium constraints (MPEC).A new constraint qualification called MPEC-pseudonormality is proposed by weakly stationary.According to a simple way,we prove that MPEC-pseudonormality is between MPEC Mangasarian-Fromovitz constraint qualification (MPEC-MFCQ) and MPEC Abadies constant qulification (MPEC-ACQ).So MPEC-pseudonormality can also derive M-stationary of MPEC.Finally,we state that the relationships among MPEC-pseudonormality,MPEC-MFCQ and MPEC-ACQ are strict. |
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| Keywords: | constraint qualification pseudonormality mathematical programs with equilibrium constraints stationary |
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