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The problem of minimizing a sum of local convex objective functions over anetworked system captures many important applications and has received muchattention in the distributed optimization field. Most of existing work focuseson development of fast distributed algorithms under the presence of a centralclock. The only known algorithms with convergence guarantees for this problemin asynchronous setup could achieve either sublinear rate under totallyasynchronous setting or linear rate under partially asynchronous setting (withbounded delay). In this work, we built upon existing literature to develop andanalyze an asynchronous Newton based approach for solving a penalized versionof the problem. We show that this algorithm converges almost surely with globallinear rate and local superlinear rate in expectation. Numerical studiesconfirm superior performance against other existing asynchronous methods.

Superlinearly Convergent Asynchronous Distributed Network Newton Method