Thevenin Decomposition 1 and Large - Scale Optimization

Thevenin’s theorem, one of the most celebrated results of electric circuit theory, provides a two-parameter characterization of the behavior of an arbitrarily large circuit, as seen from two of its terminals. We interpret the theorem as a sensitivity result in an associated minimum energy/network flow problem, and we abstract its main idea to develop a decomposition method for convex quadratic programming problems with linear equality constraints, such as those arising in a variety of contexts such as Newton’s method, interior point methods, and least squares estimation. Like Thevenin’s theorem, our method is particularly useful in problems involving a system consisting of several subsystems, connected to each other with a small number of coupling variables.