Bound Constrained Optimization
Let $x\in\mathbf{R}^n$ and $f(x)$ is a differentiable function, this application solves the bound constrained optimization: \[ \begin{aligned} \min_{x\in\mathbf{R}^n} \quad & f(x)\\ \textrm{s.t.}\quad & l\leqslant x \leqslant u \end{aligned} \] where $x_i$ is in the interval $l_i\leqslant x_i\leqslant u_i$ for $i=1,\ldots,n$.
For example, here is a problem, written in the form above, that can be solved by this calculator: \[ \begin{aligned} \min_{x\in\mathbf{R}^2} \quad & \frac{1}{3}(x_1+1)^3+x_2 \\ \textrm{s.t.}\quad & 1\leqslant x_1 \leqslant 10 \\ & 0\leqslant x_2 \leqslant 10 \end{aligned} \]
Input Data
This calculator uses the same input format as used in constrained optimization calculator, except that there are no equality constraint and no inequality constraint.