### Non-linear programming

I would like to minimize a non-linear function with Sage.

More precisely I would like to ~~minimize ~~find the numerical minimum of a function ~~of the type
~~ $\sum_{i=1}^{n} a_i \log \frac{1}{x_i}$
where the variables $x_i$ are subjected ~~to some ~~**linear** ~~constraints.~~constraints, while $a_i$ are
known coefficients.

~~I define ~~Thus the constraints are essentially similar to the ones of a ~~program with all the constraints. ~~continuous linear program. And now I would like to set up the objective function and solve.

Since that is not a linear program I wonder how to do it in Sage. Is there a ~~way?~~way? I thought that since the function is concave, a routine for convex optimization should work.