Abstract
This chapter discusses the duality for the sum of convex functions in general Banach spaces. The constraint qualification or a Slater stability condition is discussed in the chapter. The chapter also shows that the same conclusion holds under the weaker and more geometrical assumption. The chapter discusses some corollaries and points out a connection with the closed range theorem for linear operators. The theorem that holds in general Banach spaces is also emphasized. In the special case of a reflexive Banach space the proof is slightly simpler; in particular it is not necessary to invoke the Banach-Dieudonné- Krein-Smulian theorem.