Global optimization tailored for graphics processing units: Complete and rigorous search for large-scale nonlinear minimization

arXiv:2507.01770v4 Announce Type: replace-cross Abstract: This paper introduces a numerical method to enclose the global minimum of a nonlinear function subject to simple bounds on the variables. Using interval analysis, coupled with the computational power and architecture of graphics processing units (GPUs), the method iteratively rules out the regions in the search domain where the global minimum cannot exist and leaves a finite set of regions where the global minimum must exist. For effectiv