Zero duality gap for classes of DC optimization programs with polynomials

J. Vicente Pérez

In this talk we analyze some classes of difference of convex (DC) optimization programs involving polynomials. By way of generalizing the celebrated Farkas lemma to inequality systems involving the difference of a non-smooth convex function, defined by the maximum of convex polynomials over a compact convex set, and a convex polynomial, we show that there is no duality gap between this class of DC polynomial program and its associated conjugate dual problem. We then obtain strong duality under a constraint qualification. Finally, we derive some particular cases and show applications.

Keywords: DC optimization convex polynomials

G. Beer

M. Rodríguez Álvarez

M. D. Fajardo Gómez, J. Vidal Nuñez, S. M. Grad

M. Thera