On this project we will see Fenchel Duality.If the function is convex and di er-rnentiable every where,then we can nd the minimizer by setting the derivativernto zero. If the function is convex but not di erentiable, then we need morernadvanced theory. Fenchel duality is one such theory. So on this project wernwill see how to solve such kind of optimization functions/problems.