Duality

This chapter studies convex stochastic optimization within the general functional analytic duality theory of convex optimization. This will yield a dual problem whose optimum value coincides with that of the primal problem and whose optimal solutions can be used to characterize those of the primal. The purpose of this chapter is to lay out the duality framework while the remaining two chapters will give sufficient conditions for the absence of a duality gap and the existence of primal and dual solutions, respectively.