Duality in disjunctive programming via vector optimization (Q1334951)

The author develops a new duality theory for families of linear programs with an emphasis on disjunctive linear optimization by proposing a `vector' optimization problem as a dual problem. The author defines `optimal point' and `minimal value' in the context of vector optimization to prove a weak duality, a strong duality and a zero duality gap result. This treatment differs from the traditional duality principle where the dual of a scalar optimization problem is another scalar problem. The author shows that his 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 problems.