Extension of the value function reformulation to multiobjective bilevel optimization
| Autor: | Lafhim, Lahoussine, Zemkoho, Alain |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 18 pages |
| Databáze: | arXiv |
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