Optimization with an Auxiliary Constraint and Decomposition

In the context of decomposition/coordination of a linear quadratic optimal control problem, Takahara’s algorithm was an earlier version of the so-called Interaction Prediction Principle that can be examined in the more general framework of infinite-dimensional constrained optimization problems. This principle is both a decomposition principle and a coordination strategy based on a fixed point scheme. It has been later revisited in the general theory of the Auxiliary Problem Principle and the convergence of corresponding iterative algorithms has been analyzed. In this paper, we keep the same decomposition principle but we propose an alternative coordination strategy. The improvement brought by this new strategy is proved theoretically and illustrated by a numerical example. All of this is based on some manipulation of constrained optimization problems that we call the Auxiliary Constraint Principle.