Coordination in hierarchical algorithms

An analogy between hierarchical computation and the univariate method in classical nonlinear programming is brought out. This provides a basis for determining the sources of inefficiency and divergence in several coordination schemes proposed in the literature. The analogy also indicates ways of improving them. Several algorithms, both from static and dynamic (linear and nonlinear) optimization, are examined to illustrate the ideas presented. Each algorithm is used with the proposed strategy, defined as the univariate coordination and the conventional one, defined as the standard coordination, on a number of numerical examples. The gains in the computational efficiency confirm the superiority of univariate coordination. Apart from computational advantages, the analogy between hierarchical computation and the univariate method in nonlinear programming provides a rational basis for distributing the computational tasks among various levels. This is useful in deriving new multilevel optimization algorithms.