  Solving optimization problems in multi-agent systems (MAS) involves
information exchange between agents. These solutions must be robust to delays
and errors that arise from an unreliable wireless network which typically
connects the MAS. In today's large-scale dynamic Internet Of Things style
multi-agent scenarios, the network topology changes and evolves over time. In
this paper, we present a simple distributed gradient based optimization
framework and an associated algorithm. Convergence to a minimum of a given
objective is shown under mild conditions on the network topology and objective.
Specifically, we only assume that a message sent by a sender reaches the
intended receiver, possibly delayed, with some positive probability. To the
best of our knowledge ours is the first analysis under such weak general
network conditions. We also discuss in detail the verifiability of all
assumptions involved. This paper makes a significant technical contribution in
terms of the allowed class of objective functions. Specifically, we present an
analysis wherein the objective function is such that its sample-gradient is
merely locally Lipschitz continuous. The theory developed herein is supported
by numerical results. Another contribution of this paper is a consensus
algorithm based on the main framework/ algorithm. The long-term behavior of
this consensus algorithm is a direct consequence of the theory presented.
Again, we believe that ours is the first consensus algorithm to account for
unbounded stochastic communication delays, in addition to time-varying
networks.
