| 摘要: |
| 本文研究了近年提出的一类新优化问题存零约束优化问题，因存零约束的存在，使得求解最优解较困难.因此，本文针对存零约束优化问题，利用对偶理论提出了问题的Wolfe型对偶模型.在凸性和严格凸性假设下，获得了Wolfe对偶的弱、强、逆、限制逆和严格逆对偶结果.并进行了实例论证. |
| 关键词: 非线性规划 存零约束 对偶问题 广义凸性 |
| DOI： |
| 分类号:O221.2 |
| 基金项目:重庆市自然科学基金（cstc2019jcyj-msxmX0390）；重庆工商大学研究生创新型科研项目（yjscxx2022-112-184）；重庆工商大学科研项目（ZDPTTD201908）. |
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| DUALITY PROBLEM OF MATHEMATICAL PROGRAMS WITH SWITCHING CONSTRAINTS |
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LUO Mei-ling1, LI Gao-xi1, WU Chun2
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1.College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;2.College of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
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| Abstract: |
| In this paper, a new class of optimization problems proposed in recent years is studied, which makes it difficult to solve the optimal solution due to the existence of switching constraint. Therefore, this paper proposes a Wolfe type dual model by using the duality theory to solve the mathematical programs with switching constraints problem. Under the convexity and strict convexity assumptions, the weak, strong, inverse, restricted inverse and strict inverse duality results of Wolfe's duality are obtained. An example is given to demonstrate. |
| Key words: nonlinear programming switching constraint duality problem generalized convexity |
