Nonsmooth Global Optimization
Let $x\in\mathbf{R}^n$ and $f(x)$ is a continuous function, this application solves the nonsmooth global optimization problem: \[ \begin{aligned} \min_{x\in\mathbf{R}^n} \quad & f(x)\\ \textrm{s.t.}\quad & l\leqslant x \leqslant u \end{aligned} \]
This application differs from bound constrained optimization calculator in that it finds the global minimizer of continuous function, not necessary differentiable, while the latter finds a local minimizer of differentiable continuous functions $f(x)$. In the case $f(x)$ has only one minimum, the results from both calculators should be approximately the same but this application is more slower than the latter in solving the problem.
Here is an example of problems that can be solved by this calculator: \[ \begin{aligned} \min_{x\in\mathbf{R}^2} \quad & -(x_2+47)\sin\sqrt{\left|\frac{x_1}{2}+(x_2+47)\right|}-x_1\sin\sqrt{\left|x_1-(x_2+47)\right|} \\ \textrm{s.t.}\quad & -512\leqslant x_1 \leqslant 512 \\ & -512\leqslant x_2 \leqslant 512 \end{aligned} \]
Input Data
This calculator uses the same input format as used in bound constrained optimization calculator. If $l$ and $u$ are not provided, the calculator set them to -10 and 10, respectively.