Distributed Solution for a Maximum Variance Unfolding Problem with Sensor and Robotic Network Applications

Abstract—We focus on a particular non-convex networked optimization problem, known as the Maximum Variance Unfold-ing problem and its dual, the Fastest Mixing Markov Process problem. These problems are of relevance for sensor networks and robotic applications. We propose to solve both these problems with the same distributed primal-dual subgradient iterations whose convergence is proven even in the case of approximation errors in the calculation of the subgradients. Furthermore, we illustrate the use of the algorithm for sensor network applications, such as localization problems, and for mobile robotic networks applications, such as dispersion problems. I