minimize cTx subject to x ∈ A∩C,
where $x,c∈R^n$, C is a convex closed nonempty set in $R^n$, A=a+S is an affine set, where $a∈R^n$ and S is a subspace of $R^n$, and A ∩ ri(C)≠ ∅.
Use the Fenchel duality theorem to show that the dual problem can be stated as
minimize aTy
subject to y−c ∈ S⊥
In this question, what does the upside down "T" mean after the S in the final line of this question? Also, I am slightly unfamiliar with the format "cTx" and "aTy". Any help would be great.
This is the first question I've come across that asks for you to show that it is equivalent to a dual problem.