An Efficient Global Optimization Algorithm with Adaptive Estimates of the Local Lipschitz Constants

Abstract: In this work, we present a new deterministic partition-based Global Optimization (GO) algorithm that uses estimates of the local Lipschitz constants associated with different sub-regions of the domain of the objective function. The estimates of the local Lipschitz constants associated with each partition are the result of adaptively balancing the global and local information obtained so far from the algorithm, given in terms of absolute slopes. We motivate a coupling strategy with local optimization algorithms (both gradient-based and derivative-free) to accelerate the convergence speed of the proposed approach. In the end, we compare our approach HALO (Hybrid Adaptive Lipschitzian Optimization) with respect to popular GO algorithms using hundreds of test functions. From the numerical results, the performance of HALO is very promising and can extend our arsenal of efficient procedures for attacking challenging real-world GO problems. The Python code of HALO is publicly available on GitHub. \url{https://github.com/dannyzx/HALO}