Strong and Total Lagrange Dualities for Quasiconvex Programming

We consider the strong and total Lagrange dualities for infinite quasiconvex optimization problems. By using the epigraphs of thez-quasi-conjugates and the Greenberg-Pierskalla subdifferential of these functions, we introduce some new constraint qualifications. Under the new constraint qualifications, we provide some necessary and sufficient conditions for infinite quasiconvex optimization problems to have the strong and total Lagrange dualities.