Linear Programming with Set Coefficients

Linear Programming with Set Coefficients

In this paper, we investigate a linear programming problem. Our interest is focused on the case where the coecients of objective function, the coecients matrix and the right hand side vector are either compact convex sets or, in particular, convex polytopes. We are interested primarily in the systems of inequalities; later on we also deal with systems of equations. A new concept of strict feasibility and the dual case of this kind of problems is also introduced and investigated. As convexity, compactness and regularity of the coecients matrix is not sucient for strong duality; the main result of this paper deals with nding a necessary and sucient conditions for strong duality.