Optimization by decomposition and coordination: A unified approach

In the general framework of inifinite-dimensional convex programming, two fundamental principles are demonstrated and used to derive several basic algorithms to solve a so-called "master" (constrained optimization) problem. These algorithms consist in solving an infinite sequence of "auxiliary" problems whose solutions converge to the master\´s optimal one. By making particular choices for the auxiliary problems, one can recover either classical algorithms (gradient, Newton-Raphson, Uzawa) or decomposition-coordination (two-level) algorithms. The advantages of the theory are that it clearly sets the connection between classical and two-level algorithms, It provides a framework for classifying the two-level algorithms, and it gives a systematic way of deriving new algorithms.