2021/11/15 by Lahoussine Lafhim, Lafhim, Lahoussine, Alain B. Zemkoho +1
Computer Science · Engineering · #49K99 #90C26 #90C31 #90C46 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2111.07522
openalex publication_date 2021/11/15 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
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.