  The parallel solution of large scale non-linear programming problems, which
arise for example from the discretization of non-linear partial differential
equations, is a highly demanding task. Here, a novel solution strategy is
presented, which is inherently parallel and globally convergent. Each global
non-linear iteration step consists of asynchronous solutions of local
non-linear programming problems followed by a global recombination step. The
recombination step, which is the solution of a quadratic programming problem,
is designed in a way such that it ensures global convergence. As it turns out,
the new strategy can be considered as a globalized additively preconditioned
inexact Newton (ASPIN) method. However, in our approach the influence of
ASPIN's non-linear preconditioner on the gradient is controlled in order to
ensure a sufficient decrease condition. Two different control strategies are
described and analyzed. Convergence to first-order critical points of our
non-linear solution strategy is shown under standard trust-region assumptions.
The strategy is investigated along difficult minimization problems arising from
non-linear elasticity in 3D solved on a massively parallel computer with
several thousand cores.
