a1 Department of Mathematics, Dalhousie University, Halifax, Canada
a2 Department of Mathematics, University of Alberta, Edmonton, Canada
In this paper we study the abstract convex program
where S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.
(Received March 21 1980)
(Revised July 28 1980)
1980 Mathematics subject classification (Amer. Math. Soc.)