Distributed Optimization of Convex Sum of Non-Convex Functions
  We present a distributed solution to optimizing a convex function composed of several non-convex functions. Each non-convex function is privately stored with an agent while the agents communicate with neighbors to form a network. We show that coupled consensus and projected gradient descent algorithm proposed in [1] can optimize convex sum of non-convex functions under an additional assumption on gradient Lipschitzness. We further discuss the applications of this analysis in improving privacy in distributed optimization. 
Shripad Gade and Nitin H. Vaidya
cs.DC cs.LG math.OC