A duality theory for infinite-horizon optimization of concave input/ouput processes

A general concave ∞-horizon optimization model is analyzed with the help of a special convexity concept, which combines both the usual convexity and the dynamic structure. The axiomatic setup leads to a perfect symmetry between the primal and dual problems. After introducing a particular dynamic feasibility hypothesis, the following results are presented: (i) boundedness of trajectories as a necessary condition for optimally, (ii) the existence of primal and dual optimal trajectories, (iii) approximation by finite horizon models, and (iv) necessary and sufficient conditions for optimality.