带有极值函数的多目标双层规划问题的对偶

Duality for Multiobjective Bilevel Programming Problems with Extremal-Value Function

中文关键词:  多目标优化  双层规划问题  共轭对偶  凸规划  复合凸函数

英文关键词:multiobjective optimization  bilevel programming problems  conjugate duality  convex programming  composed convex functions

中文摘要:

      本文利用Fenchel-Moreau共轭函数建立了带有极值函数的多目标双层规划问题的对偶问题.在凸性和单调性的假设下,得到了原问题与对偶问题的弱对偶和强对偶结论.

英文摘要:

      For a multiobjective bilevel programming problem $(P)$ with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.