Different conjugate dual problems in vector optimization and their relations
The authors study a problem of minimizing a vector function \(f(x)\) under a set constraint \(x\in E\) and an inclusion constraint \(g(x)\in -D\) where \(D\) is a closed pointed cone with a nonempty interior. They construct three kinds of dual problems by using conjugate maps associated with perturbation in the objective \(f(x+p)\), in the constraint \(g(x)\in -(D+q)\) and their combination. Weak duality, strong duality and some inclusion relations for optimal values of these dual problems are established.
scientific article; zbMATH DE number 5550748
scientific article