
Journal of Convex Analysis 07 (2000), No. 1, 047072 Copyright Heldermann Verlag 2000 EpiDistance Convergence of Parametrised Sums of Convex Functions in NonReflexive Spaces A. Eberhard Dept. of Mathematics, Royal Melbourne University of Technology, Melbourne 3001, Australia R. Wenczel Dept. of Mathematics, Royal Melbourne University of Technology, Melbourne 3001, Australia A weak set of conditions ensuring epidistance convergence of the sum of two epidistance convergent families of closed convex functions, are established. These conditions may be viewed as containing two parts. The first is that zero is in the strong quasirelative interior of difference of the domains of the epidistance limits of these families, a condition which has been used elsewhere in YoungFenchel duality. The second part implies (and is essentially equivalent to) the epidistance convergence of the subspaces generated by the closure of the span of the differences of domains of the corresponding pairs of functions taken from these families. Convergence of saddle points in YoungFenchel duality is investigated. Although both functions may vary in a very general way it is shown one can always extract a convergent subsequence of dual optimal solutions when both sequences of convex functions epiconverge and satisfy the conditions outlined above. [ Fulltextpdf (298 KB)] 