Complexity of circumscribed and inscribed ellipsoid methods for solving equilibrium economical models

摘要

An exchange-production model and the Arrow-Debreu model with linear utility functions are considered. These models are reduced to special convex programming problems. These problems can be solved by the inscribed and circumscribed ellipsoid methods. It is proved that the inscribed ellipsoid method's complexity, in this case, is less than the complexity of the circumscribed ellipsoid method.