In this paper we propose an original proof of Mehler expansion of the Gaussian distribution in terms of probabilistic Hermite polynomials.

Primal or dual strong-duality (or min-sup, inf-max duality) in nonconvex optimization is revisited in view of recent literature on the subject, establishing, in particular, new characterizations for the second case. This gives rise to a new class of quasiconvex problems having zero duality gap or closedness of images of vector mappings associated to those problems. Such conditions are described for the classes of linear fractional functions and that of quadratic ones. In addition, some applications to nonconvex quadratic optimization problems under a single inequality or equality constraint, are presented, providing new results for the fulfillment of zero duality gap or dual strong-duality.

Poster presented at the 2021 CEDAR Virtual Workshop, June 20-25.