CONVERGENCE AND NUMERICAL RESULTS FOR A PARALLEL ASYNCHRONOUS QUASI-NEWTON METHOD

During the execution of a parallel asynchronous iterative algorithm, each task does not wait for predetermined data to become available. On the contrary, they can be viewed as local and independent iterative algorithms, which perform their own iterative scheme on the data currently available. On the basis of this computational model, a parallel asynchronous version of the quasi-Newton method for solving unconstrained optimization problems is proposed. The algorithm is based on four tasks concurrently executing and interacting in an asynchronous way. Convergence conditions are established and numerical results are presented which prove the effectiveness of the proposed parallel asynchronous approach.