Minima distribution for global optimization

Minima distribution (MD) establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known connection $\nabla f(x^*)=0$ between a differentiable convex function $f$ and its minimizer $x^*$. MD theory provides us with a global monotonic convergence for the minimization of continuous functions on compact sets without any other assumptions; and the asymptotic convergence rate can be further determined for twice continuously differentiable functions. Moreover, a derivative-free algorithm based on MD theory is proposed for finding a stable global minimizer of a possibly highly nonlinear and non-convex function. Numerical experiments are performed for several illustrative examples, and a MATLAB code that demonstrates how the proposed algorithm works is provided in appendix for readers' convenience.