集值优化问题严最大有效解的高阶刻画

运筹学学报 ›› 2011, Vol. 15 ›› Issue (2): 103-109.

集值优化问题严最大有效解的高阶刻画

杨扬, 徐义红, 熊卫芝

出版日期:2011-06-15 发布日期:2011-06-15
基金资助:
国家自然科学基金(10461007)；江西省自然科学基金(2009GZS0021)；江西省教育厅科技项目(GJJ09069).

Higher-Order Characterizations for Set-Valued Optimization on Strictly Maximal Efficient Solutions

YANG Yang, XU Yi-Hong, XIONG Wei-Zhi

Online:2011-06-15 Published:2011-06-15

摘要/Abstract

摘要： 在实赋范线性空间中考虑集值优化问题的严有效性.利用高阶导数的性质给出了受约束于固定集的集值优化问题取得严最大有效解的高阶导数型最优性必要条件.当目标函数为锥凹集值映射时,利用严最大有效点的性质得到集值优化问题取得严最大有效解的充分条件.

关键词: 严最大有效解, m-阶Contingent切导数, 集值优化

Abstract: The strict efficiency of set-valued optimization is considered in real normed spaces. By applying the properties of higher-order derivatives, higher-order type necessary optimality condition is established for a set-valued optimization problem whose constraint condition is determined by a fixed set to attain its strictly maximal efficient solution. When objective function is concave, with the properties of strictly maximal efficient point, sufficient optimality condition is also derived.

Key words: strictly maximal efficient solution, mth-order contingent derivative, set-valued optimization

中图分类号:

杨扬, 徐义红, 熊卫芝. 集值优化问题严最大有效解的高阶刻画[J]. 运筹学学报, 2011, 15(2): 103-109.

YANG Yang, XU Yi-Hong, XIONG Wei-Zhi. Higher-Order Characterizations for Set-Valued Optimization on Strictly Maximal Efficient Solutions[J]. Operations Research Transactions, 2011, 15(2): 103-109.

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