Distributed Adaptive Optimization with Weight-Balancing

This paper addresses the continuous-time distributed optimization of a strictly convex summation-separable cost function with possibly non-convex local functions over strongly connected digraphs. Distributed optimization methods in the literature require convexity of local functions, or balanced weights, or vanishing step sizes, or algebraic information (eigenvalues or eigenvectors) of the Laplacian matrix. The solution proposed here covers both weight-balanced and unbalanced digraphs in a unified way, without any of the aforementioned requirements.