| 集值优化问题超有效解的Lagrange最优性条件 |
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| 引用本文： | 徐义红,朱传喜.集值优化问题超有效解的Lagrange最优性条件[J].应用泛函分析学报,2005,7(4):339-343. |
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| 作者姓名： | 徐义红 朱传喜 |
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| 作者单位： | 南昌大学数学系,江西,南昌,330047 |
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| 基金项目： | 国家自然科学基金（10461007）;南昌大学基础理论基金项目 |
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| 摘 要： | 在局部凸空间中考虑约束集值优化问题（VP）在超有效解意义下的Lagrange最优性条件．在近似锥-次类凸假设下，利用择一性定理得到了（VP）取得强有效解的必要条件，利用超有效解集的性质及超有效解的定义给出了（VP）取得超有效解的充分条件，最后给出了一种与（VP）等价的无约束规划．
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| 关 键 词： | 超有效性 近似锥-次类凸性 集值优化 锥 |
| 文章编号： | 1009-1327（2005）04-0339-05 |
| 收稿时间： | 2004-02-20 |
| 修稿时间： | 2004年2月20日 |
Lagrange Optimality Conditions for Set-Valued Optimization Problem in the Sense of Superly Efficient Solutions |
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| XU Yi-hong,ZHU Chuan-xi.Lagrange Optimality Conditions for Set-Valued Optimization Problem in the Sense of Superly Efficient Solutions[J].Acta Analysis Functionalis Applicata,2005,7(4):339-343. |
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| Authors: | XU Yi-hong ZHU Chuan-xi |
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| Abstract: | Lagrange optimality conditions for the set-valued optimization problem (VP) with constraints are considered in the sense of superly efficient solutions in locally convex spaces. Under the assumption of nearly cone-subconvexlikeness, by applying alternative theorem, a Lagrange optimality necessary condition for (VP) is derived, by using properties of the set of superly efficient solutions and the definition of superly efficient solution, a sufficient condition is also obtained. Finally, a kind of unconstrained program equivalent to (VP) is established. . |
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| Keywords: | super efficiency nearly cone-subconvexlikeness set-valued optimization cone |
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