Maximal domains of quasi-convexity and pseudo-convexity for quadratic functions

We study quasi-convex and pseudo-convex quadratic functions on solid convex sets. This generalizes Martos' results in [12] and [13] by using Koecher's results in [8].This research was supported by Hydro—Quebec; University of Montreal; Office of Naval Research, Contract N-00014-47-A0112-0011; National Science Foundation, Grant GP 25738.