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Explore a comprehensive lecture on the progressive decoupling algorithm in convex optimization, focusing on its application to optimal control problems. Delve into the adaptation of the proximal point algorithm for iteratively suppressing linkage constraints in convex function minimization. Examine how this decoupling process in optimal control leads to solving parallel optimization subproblems centered on individual time instants. Discover the ideal continuous-time version of the procedure and its potential discrete-time approximations. Gain insights into the connections between classical calculus of variations concepts and their modern interpretations through convex analysis and the Legendre-Fenchel transform. Understand how this broader framework enables the flourishing of duality in optimization theory. This 34-minute talk, presented by Terry Ralph Rockafellar at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), was part of the "One World Optimization Seminar in Vienna" workshop held in June 2024.
