Distributed Nonconvex Optimization of Multiagent Systems Using Boosting Functions to Escape Local Optima

Abstract

In this article, we address the problem of multiple local optima arising due to nonconvex objective functions in cooperative multiagent optimization problems. To escape such local optima, we propose a systematic approach based on the concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">boosting functions</i> . The underlying idea is to temporarily transform the gradient at a local optimum into a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">boosted</i> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gradient</i> with a nonzero magnitude. We develop a distributed boosting scheme based on a gradient-based optimization algorithm using a novel optimal variable step size mechanism so as to guarantee convergence. Even though our motivation is based on the coverage control problem setting, our analysis applies to a broad class of multiagent problems. Simulation results are provided to compare the performance of different boosting functions families and to demonstrate the effectiveness of the boosting function approach in attaining improved (still generally local) optima.