Statistical Analysis on Global Optimization

The global optimization of a mathematical model determines the best parameters such that a target or cost function is minimized. Optimization problems arise in almost all scientific disciplines (operations research, life sciences, etc.). Only in a few exceptional cases, these problems can be solved analytically-exactly, so in practice numerical routines based on approximations have to be used. The routines return a result -- a so-called candidate of a global minimum. Unfortunately, the question whether the candidate represents the optimal solution, often remains unanswered. This article presents a simple-to-use, statistical analysis that determines and assesses the quality of such a result. This information is valuable and important -- especially for practical application.