Duality in disjunctive programming via vector optimization

Abstract

In this paper, we develop a new duality theory for families of linear programs with an emphasis on disjunctive linear optimization by proposing a ‘vector’ optimization problem as dual problem. We establish that the well-known relations between primal and dual problems hold in this context. We show that our method generalizes the duality results of Borwein on families of linear programs, of Balas on disjunctive programs, and of Patkar and Stancu-Minasian on disjunctive linear fractional programs. Moreover, we can derive some duality results for integer and for fractional programs where the denominator is not assumed (as usual) to be greater than zero for each feasible point.