Global Optimization

Global optimization seeks the best solution over an entire search space, including nonconvex landscapes with many local minima, costly evaluations, noise, or constraints. Methods range from branch-and-bound and convex relaxations that provide certificates to Bayesian optimization and hierarchical partitioning for black-box functions, as well as evolutionary, annealing, and learned search strategies. Applications include control, vision and pose estimation, clustering, engineering design, and combinatorial problems, evaluated by solution quality, feasibility, computational cost, and recovery of multiple optima. A central tension is that rigorous guarantees can be costly in high dimensions, while scalable heuristics may find strong candidates without proving global optimality; initialization, reachable regions, and benchmark realism also affect such claims.