Lecture 16: Strong duality

In the last lecture we saw how to formulate a dual program for an optimization problem. From the formulation, it turned out that the dual program gave an upper/lower bound depending on whether the problem was maximization/minimization respectively. Today, the focus will be on when are these bounds tight. It turns out that these bounds are tight in most of the cases of interest like linear programming and semidefinite programming. The previous statement is almost true except in few contrived cases. When the primal and dual values agree, strong duality is said to hold. We will look at the conditions under which strong duality holds. Lets look at the primal-dual pair for semidefinite programming.