A decomposition algorithm for unconstrained optimization problems with partial derivative information

In this paper we consider the problem of minimizing a nonlinear function using partial derivative knowledge. Namely, the objective function is such that its derivatives with respect to a pre‐specified block of variables cannot be computed. To solve the problem we propose a block decomposition method that takes advantage of both derivative‐free and derivative‐based iterations to account for the features of the objective function. Under standard assumptions, we manage to prove global convergence of the method to stationary points of the problem.