Image space analysis and scalarization of multivalued optimization (Q1035941)

Based on generalized sections of feasible sets, this paper presents optimality conditions for set-valued optimization problems of the form \[ \min_{x\in R}\,F(x),\tag{P} \] where \(R= \{x\in U: G(x)\cap(-D)\neq\emptyset\}\), and \(F: U\to Y\), \(G: U\to Z\), are set-valued mappings, with \(C\subseteq Y\), \(D\subseteq Z\) being pointed, closed, convex cones having non-empty interior, and \(Y\), \(Z\) are normed linear spaces. The notions of solutions to (P) considered are the feeble minimizer, feeble weak minimizer. Additionally, some optimality conditions for Borwein's superefficient and strongly proper solution through scalarization, are also established.