| 消失约束数学规划拉格朗日型对偶与鞍点最优性判据（英文） |
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| 引用本文： | 胡清洁,董榕恩,张海琦.消失约束数学规划拉格朗日型对偶与鞍点最优性判据（英文）[J].应用数学,2019,32(3):608-618. |
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| 作者姓名： | 胡清洁 董榕恩 张海琦 |
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| 作者单位： | 广西自动检测技术与仪器重点实验室;广西高校数据分析与计算重点实验室;桂林电子科技大学数学与计算科学学院 |
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| 基金项目： | Supported by the NNSF(11461015,11761014)of China;the Guangxi Natural Science Foundation(2015GXNSFAA139010,2017GXNSFAA198243);the Innovation Project for Postgraduate of Guilin University of Electronic Technology(2017YJCX82) |
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| 摘 要： | 本文基于消失约束的结构特征,提出消失约束数学规划一个不涉及未知指标集的拉格朗日型对偶,并在合适条件下建立了弱对偶和强对偶定理.另外,也讨论了消失约束数学规划的鞍点最优性判据.最后,我们通过某些例子验证了这些结果的合理性.
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| 关 键 词： | 消失约束数学规划 拉格朗日对偶 鞍点最优性判据 |
| 收稿时间： | 2018/8/2 0:00:00 |
Lagrange Type Duality and Saddle Point Optimality Criteria for Mathematical Programs with Vanishing Constraints |
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| HU Qingjie,DONG Rongen,ZHANG Haiqi.Lagrange Type Duality and Saddle Point Optimality Criteria for Mathematical Programs with Vanishing Constraints[J].Mathematica Applicata,2019,32(3):608-618. |
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| Authors: | HU Qingjie DONG Rongen ZHANG Haiqi |
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| Institution: | (Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin 541004, China;Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin 541004, China;School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China) |
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| Abstract: | In this paper, based on the structure characteristic of vanishing constraints, we propose a Lagrange type dual model which does not include the unknown index sets for the mathematical programs with vanishing constraints and establish the weak, strong duality results between the primal problem and the Lagrange type dual model under mild assumptions. We also investigate the optimality criteria of the saddle point problem to the mathematical programs with vanishing constraints under some conditions. Finally, we also verify the validity of these results through some examples. |
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| Keywords: | Mathematical programs with vanishing constraints Lagrange duality Saddle point optimality criteria |
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