Global Convergence Of The Partitioned BFGS Algorithm For Convex Partially Separable Optimization.

Global convergence is proved for a partitioned BFGS algorithm, when applied on a partially separable problem with a convex decomposition. This case covers a known practical optimization method for large dimensional unconstrained problems. Inexact solution of the linear system defining the search direction and variants of the steplength rule are also shown to be acceptable without affecting the global convergence properties.