| 拟不变凸集值优化的Kuhn-Tucker条件与Wolfe对偶 |
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| 引用本文： | 盛宝怀,刘三阳.拟不变凸集值优化的Kuhn-Tucker条件与Wolfe对偶[J].应用数学和力学,2006,27(12):1447-1456. |
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| 作者姓名： | 盛宝怀 刘三阳 |
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| 作者单位： | 绍兴文理学院 数学系, 浙江 绍兴 312000;2.西安电子科技大学 应用数学系,西安 710071 |
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| 基金项目： | 国家自然科学基金;浙江省自然科学基金 |
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| 摘 要： | 研究了拟不变凸集值优化最优性的Kuhn-Tucker条件及Wolfe型对偶问题．首先引进了alpha-阶G-拟不变凸集和alpha-阶S-拟不变凸集值函数的概念,由此研究了alpha-阶G-拟不变凸集所对应的伴随切锥及alpha-阶伴随导数的性质;最后,借助alpha-阶伴随切导数刻画了alpha-阶S-拟不变凸集值优化最优性的Kuhn-Tucker条件和Wolfe型对偶．
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| 关 键 词： | 拟不变凸集值函数 伴随上图导数 最优性条件 对偶 |
| 文章编号： | 1000-0887（2006）12-1447-10 |
| 收稿时间： | 2004-09-17 |
| 修稿时间： | 2006-08-19 |
Kuhn-Tucker Condition and the Wolfe Duality of Preinvex Set-Valued Optimization |
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| SHENG Bao-huai,LIU San-yang.Kuhn-Tucker Condition and the Wolfe Duality of Preinvex Set-Valued Optimization[J].Applied Mathematics and Mechanics,2006,27(12):1447-1456. |
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| Authors: | SHENG Bao-huai LIU San-yang |
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| Institution: | Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, P. R. China; |
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| Abstract: | The optimality Kuhn-Tucker condition and the Wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order Spreinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied; Then, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative. |
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| Keywords: | preinvex set-valued fimction contingent epiderivatives optimality conditions duality |
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