I have a problem finding a solver that can solve a mathematical programming model with a quasi quadratic object function. I have tried some commercially available quadratic and non-linear solvers, but they have all turned out unfeasible solutions. The model has the following object function with:
$$\mbox{Min} [Z] = \sum_i (x(i)^2 + a( e^{d\,x(i)} – x(i) – 1)) ; $$
$i = 0.....n$; and with linear constraints.
The function is continuous and has a single minimum at $x = 0$ with $dZ/dx=0$. At $a = 0$ this is a true quadratic function. I assumed that a quadratic solver could solve this but those I tried failed.
I want to know if someone could recommend a suitable solver to this problem?