Duality gap in convex programming (Q1881045)

The author gives a condition called property D which ensures that there is no duality gap between the general convex programming problem and its dual. The property D is stated in the general setting of quasiconvex functions over a normed vector space and then adapted for the case of convex functions in the finite-dimensional space. This is followed by establishing existence results for functions satisfying property D. It is claimed these generalize known results including those of \textit{R. T. Rockafellar} [J. Optimization Theory Appl. 7, 143--148 (1971; Zbl 0198.24604)] and \textit{A. Auslender} [Math. Program. 88, No. 1(A), 45--59 (2000; Zbl 0980.90063)].