  We address the problem of multiple local optima commonly arising in
optimization problems for multi-agent systems, where objective functions are
nonlinear and nonconvex. For the class of coverage control problems, we propose
a systematic approach for escaping a local optimum, rather than randomly
perturbing controllable variables away from it. We show that the objective
function for these problems can be decomposed to facilitate the evaluation of
the local partial derivative of each node in the system and to provide insights
into its structure. This structure is exploited by defining "boosting
functions" applied to the aforementioned local partial derivative at an
equilibrium point where its value is zero so as to transform it in a way that
induces nodes to explore poorly covered areas of the mission space until a new
equilibrium point is reached. The proposed boosting process ensures that, at
its conclusion, the objective function is no worse than its pre-boosting value.
However, the global optima cannot be guaranteed. We define three families of
boosting functions with different properties and provide simulation results
illustrating how this approach improves the solutions obtained for this class
of distributed optimization problems.
