  Decentralized optimization has found a significant utility in recent years,
as a promising technique to overcome the curse of dimensionality when dealing
with large-scale inference and decision problems in big data. While these
algorithms are resilient to node and link failures, they however, are not
inherently Byzantine fault-tolerant towards insider data injection attacks.
This paper proposes a decentralized robust subgradient push (RSGP) algorithm
for detection and isolation of malicious nodes in the network for optimization
non-strongly convex objectives. In the attack considered in this work, the
malicious nodes follow the algorithmic protocols, but can alter their local
functions arbitrarily. However, we show that in sufficiently structured
problems, the method proposed is effective in revealing their presence. The
algorithm isolates detected nodes from the regular nodes, thereby mitigating
the ill-effects of malicious nodes. We also provide performance measures for
the proposed method.
