SMGO: A set membership approach to data-driven global optimization

Many science and engineering applications feature non-convex optimization problems where the objective function cannot 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.