Lipschitz global optimization problems using direct-type algorithms and diagonal partitioning strategies

Abstract

This thesis proposes a new global optimization algorithm called BIRECT-V (V for vertices),inspired by the recently introduced BIRECT (BIsection of RECTangles)algorithm. It combines bisection with a two-point sampling strategy, strategically positioning the sampling points at 1/3 and 1 along the primary diagonal within the initial hyper-rectangle. This approach provides a more comprehensive understanding of the objective function compared to single-point sampling.The BIRECT-V algorithm presents a promising new approach to global optimization, effectively addressing the limitations of existing DIRECT-type algorithms in handling complex optimization problems.Its combination of bisection with a two-point sampling strategy,coupled with the proposed domain modification to prevent redundant function evaluations,makes it a powerful tool for solving a wide range of optimization problems, particularly in high-dimensional settings.