Distributed Non-convex Optimization of Multi-agent Systems Using Boosting Functions to Escape Local Optima

We address the problem of multiple local optima arising in cooperative multi-agent optimization problems with non-convex objective functions. We propose a systematic approach to escape these local optima using boosting functions. These functions temporarily transform a gradient at a local optimum into a "boosted" non-zero gradient. Extending a prior centralized optimization approach, we develop a distributed framework for the use of boosted gradients and show that convergence of this distributed process can be attained by employing an optimal variable step size scheme for gradient-based algorithms. Numerical examples are included to show how the performance of a class of multi-agent optimization systems can be improved.