| 多目标优化问题Proximal真有效解的最优性条件 |
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| 引用本文： | 李小燕,高英.多目标优化问题Proximal真有效解的最优性条件[J].应用数学和力学,2015,36(6):668-676. |
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| 作者姓名： | 李小燕 高英 |
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| 作者单位： | 重庆师范大学 数学学院, 重庆 400047 |
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| 基金项目： | 国家自然科学基金(11201511；11271391；11431004) |
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| 摘 要： | 在广义凸性假设下，给出了集合proximal真有效点的线性标量化，并在此基础上证明了它与Benson真有效点和Borwein真有效点的等价性.将这些结果应用到多目标优化问题上，得到proximal真有效解的最优性条件.最后，利用proximal次微分，得到了proximal真有效解的模糊型最优性条件.
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| 关 键 词： | proximal法锥 多目标优化 proximal真有效解 最优性条件 |
| 收稿时间： | 2014-12-08 |
Optimality Conditions for Proximal Proper Efficiency in Multiobjective Optimization Problems |
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| LI Xiao-yan,GAO Ying.Optimality Conditions for Proximal Proper Efficiency in Multiobjective Optimization Problems[J].Applied Mathematics and Mechanics,2015,36(6):668-676. |
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| Authors: | LI Xiao-yan GAO Ying |
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| Institution: | College of Mathematics Science, Chongqing Normal University, Chongqing 400047, P.R.China |
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| Abstract: | First, linear scalarization of the proximal proper efficient points to a closed set was presented under the generalized convexity assumption, and the equivalency among the proximal proper efficiency, Benson proper efficiency and Borwein proper efficiency in multiobjective optimization problems was proved. Second, the optimality conditions for multiobjective optimization problems were obtained through application of these results to the problems. Finally, the fuzzy optimality conditions for the proximal proper efficient solutions were given with the proximal subdifferential. |
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| Keywords: | proximal normal cone multiobjective optimization problem proximal proper efficiency optimality condition |
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