Closing the duality gap in linear vector optimization. (English) Zbl 1063.90047
The paper considers the duality theory in linear vectorial programming by using the Lagrangean approach without scalarization. The dual problem has set-valued nature. The aim of the paper is to use methods of set-valued optimization for deriving duality assertions in linear vector optimization. A case study parallel to the scalar linear optimization is presented. The proofs are based onto a separation property introduced by the authors. The main features of the theory are illustrated by simple examples.
Reviewer: Francisco Guerra Vazquez (Puebla)
MSC:
90C29 | Multi-objective and goal programming |
90C46 | Optimality conditions and duality in mathematical programming |
90C05 | Linear programming |