CONJUGATE DUALITY FOR CONCAVE MAXIMIZATION PROBLEMS AND APPLICATIONS

Abstract

In this article, we present a conjugate duality for scalarmaximization and vectormaximization problems involving concave increasing continuous homogeneous functions. We will show that the obtained conjugate duality has zero-gap and a duality inequality helps to characterize the weakly Pareto efficient for the vector-maximization problem. As a result, an optimization problem over the weakly efficient set reduces to a bilevel optimization problem solvable by monotonic optimization methods.