The progressive decoupling algorithm in convex optimization is an adaptation of the proximal point algorithm for iteratively suppressing linkage constraints in the minimization of a convex function. In optimal control, linkages appear in the relationship between states and controls at different times, and their decoupling leads to solving, in parallel, optimization subproblems focused on single instants of time. An ideal version of the procedure will be described in continuous time along with its possibilities for approximation in discrete time. Along the way, connections will be made between classical ideas in the calculus of variations and their translation, through convex analysis and the Legendre-Fenchel transform, into a much broader modern format in which duality can flourish.