An easy way to obtain strong duality results in linear, linear semidefinite and linear semi-infinite programming

In linear programming it is known that an appropriate non-homogeneous Farkas Lemma leads to a short proof of the strong duality results for a pair of primal and dual programs. By using a corresponding generalized Farkas lemma we give a similar proof of the strong duality results for semidefinite programs under constraint qualifications. The proof includes optimality conditions. The same approach leads to corresponding results for linear semi-infinite programs. For completeness, the proofs for linear programs and the proofs of all auxiliary lemmata for the semidefinite case are included