Optimality for Set Functions with Values in Ordered Vector Spaces

[[abstract]]Let (X, F,/z) be a finite atomless measure space, 5e a convex subfamily of F, and Y and Z locally convex Hausdortt topological vector spaces which are ordered by the cones C and D, respectively. Let F:5�-~ Y be C-convex and G:oW~ Z be D-convex set functions. Consider the following optimization problem (P): minimize F(f~), subject to i2cff and G(l)) ---o 0. The paper generalizes the Moreau- Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied