Before revision:  In order to compute market equilibria, we introduce (infinite-dimensional) convex programs over Banach spaces, thereby generalizing the Eisenberg-Gale convex program and its dual . Regarding the new convex programs, we establish existence of optimal solutions, the existence of KKT-type conditions , as well as strong duality .
After revision:  In order to compute market equilibria, we introduce (infinite-dimensional) convex programs over Banach spaces, thereby generalizing the Eisenberg-Gale convex program and its dual to this infinite-dimensional setting, which leads to Banach-space optimization problems. We establish existence of optimal solutions, the existence of KKT-type conditions , as well as strong duality .