Absence of a Duality Gap

This chapter gives sufficient conditions for the existence of optimal primal solutions and for the closedness of its optimum value function and thus, for the absence of a duality gap. In general, the given conditions do not imply the existence of dual solutions; that will be the topic of Chap. 5 . Existence of dual solutions fails e.g. in many popular models of financial mathematics where, nevertheless, one obtains the existence of optimal trading strategies and the absence of a duality gap.