  The Distributed Adaptive Signal Fusion (DASF) framework is a meta-algorithm
for computing data-driven spatial filters in a distributed sensing platform
with limited bandwidth and computational resources, such as a wireless sensor
network. The convergence and optimality of the DASF algorithm has been
extensively studied under the assumption that an exact, but possibly
impractical solver for the local optimization problem at each updating node is
available. In this work, we provide convergence and optimality results for the
DASF framework when used with an inexact, finite-time solver such as (proximal)
gradient descent or Newton's method. We provide sufficient conditions that the
solver should satisfy in order to guarantee convergence of the resulting
algorithm, and a lower bound for the convergence rate. We also provide
numerical simulations to validate these theoretical results.
