  We present a convex solution for the design of generalized accelerated
gradient algorithms for strongly convex objective functions with Lipschitz
continuous gradients. We utilize integral quadratic constraints and the Youla
parameterization from robust control theory to formulate a solution of the
algorithm design problem as a convex semi-definite program. We establish
explicit formulas for the optimal convergence rates and extend the proposed
synthesis solution to extremum control problems.
