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

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 via experiments, or costly finite elements simulations. To solve these problems, global routines are used. These iterative techniques must trade-off exploitation close to current best point with exploration of unseen regions search space. In this respect, new strategy based on Set Membership (SM) framework proposed. Assuming Lipschitz continuity cost function, approach employs SM concepts decide whether switch from an mode one, vice-versa. The resulting algorithm, named SMGO (Set Global Optimization) presented. Theoretical properties regarding convergence computational complexity derived, implementation aspects discussed. Finally, performance evaluated set benchmark compared those other approaches.