  Many science and engineering applications feature non-convex optimization
problems where the objective function can not be handled analytically, i.e. it
is a black box. Examples include design optimization via experiments, or via
costly finite elements simulations. To solve these problems, global
optimization routines are used. These iterative techniques must trade-off
exploitation close to the current best point with exploration of unseen regions
of the search space. In this respect, a new global optimization strategy based
on a Set Membership (SM) framework is proposed. Assuming Lipschitz continuity
of the cost function, the approach employs SM concepts to decide whether to
switch from an exploitation mode to an exploration one, and vice-versa. The
resulting algorithm, named SMGO (Set Membership Global Optimization) is
presented. Theoretical properties regarding convergence and computational
complexity are derived, and implementation aspects are discussed. Finally, the
SMGO performance is evaluated on a set of benchmark non-convex problems and
compared with those of other global optimization approaches.
