Branch-and-bound techniques for multidimensional optimization problems

Abstract

This work addresses the global optimization of nonconvex, non-differentiable, Hölder continuous functions. We review the relevant theoretical foundations and present the classical branch-and-bound method for global optimization, alongside the reducing transformation method, which constructs 𝛼-dense curves to simplify multidimensional problems. A hybrid algorithm combining these two methods for Hölder functions is proposed, its convergence is mathematically proven, and numerical applications are presented to confirm its effectiveness compared to classical approaches.