Strong duality for standard convex programs

A primal optimization problem and its dual are in strong duality if either one of the problems has a finite optimal value, then the other one is consistent and has the same optimal value, and the optimal value of the dual problem is attained. In this paper, we study the strong duality without constraint qualifications for a standard convex optimization problem using the bifunction, image space analysis, and polynomial ring approaches. We obtain new strong duals for the primal convex optimization problem, which to the best of our knowledge have not been appeared in the related literature.