Existence of Dual Solutions

This chapter gives sufficient conditions for subdifferentiability of the optimum value function of the primal problem as defined in Sect. 3.3 . As we saw there, the subdifferentiability implies the absence of a duality gap and the existence of dual solutions. The scenariowise optimality conditions in Corollary 3.35 are then necessary as well as sufficient for optimality of feasible solutions in the primal.