  We address the problem of distributed convex unconstrained optimization over
networks characterized by asynchronous and possibly lossy communications. We
analyze the case where the global cost function is the sum of locally coupled
local strictly convex cost functions. As discussed in detail in a motivating
example, this class of optimization objectives is, for example, typical in
localization problems and in partition-based state estimation. Inspired by a
generalized gradient descent strategy, namely the block Jacobi iteration, we
propose a novel solution which is amenable for a distributed implementation and
which, under a suitable condition on the step size, is provably locally
resilient to communication failures. The theoretical analysis relies on the
separation of time scales and Lyapunov theory. In addition, to show the
flexibility of the proposed algorithm, we derive a resilient gradient descent
iteration and a resilient generalized gradient for quadratic programming as two
natural particularizations of our strategy. In this second case, global
robustness is provided. Finally, the proposed algorithm is numerically tested
on the IEEE 123 nodes distribution feeder in the context of partition-based
smart grid robust state estimation in the presence of measurements outliers.

Optimization and Control;Systems and Control;Systems and Control