Extension of the value function reformulation to multiobjective bilevel optimization
Extension of the value function reformulation to multiobjective bilevel optimization
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DOI：
10.1007/s11590-022-01948-9
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发表时间：
2021-11
影响因子：
1.6
通讯作者：
L. Lafhim;Alain B. Zemkoho
中科院分区：
文献类型：
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作者：
L. Lafhim;Alain B. Zemkoho
本文考虑一个具有向量值上下层目标函数的多目标双层优化问题。近年来，这些问题引起了人们的极大兴趣。然而，到目前为止，标量化似乎是用于处理低层问题的主要方法。在这里，我们利用边界映射的概念，扩展了最优值函数的概念，我们的参数多目标低级别的问题。在此基础上，我们建立了一个易于处理的约束资格，我们使用它来推导出问题的必要最优性条件。随后，我们表明，我们所得到的必要的最优性条件代表了一个自然的扩展，从标准的乐观的双层计划与标量目标函数。
We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the main approach used to deal with the lower-level problem. Here, we utilize the concept of frontier map that extends the notion of optimal value function to our parametric multiobjective lower-level problem. Based on this, we build a tractable constraint qualification that we use to derive necessary optimality conditions for the problem. Subsequently, we show that our resulting necessary optimality conditions represent a natural extension from standard optimistic bilevel programs with scalar objective functions.