Linear programming relaxation for quasiconvex programming

In this paper, we study linear programming relaxation for quasiconvex programming in terms of generators of quasiconvex functions. We recall linear transformation of quasiconvex inequality systems in terms of a generator. We introduce a relaxed objective function by using generators. We investigate a relaxed problem with finitely many linear constraints by using generators of constraint functions. Finally, we show the existence of exact linear programming relaxation for quasiconvex programming. In addition, we show exact linear programming relaxation for convex programming as an application of our results.