The problem is$$\max  f(\mathbf{x}) \text{ subject to } \mathbf{Ax} = \mathbf{b}$$where $f(\mathbf{x}) = \sum_{i=1}^N\sqrt{1+\frac{x_i^4}{(\sum_{i=1}^{N}x_i^2)^2}}$, $\mathbf{x} = [x_1,x_2,...,x_N]^T \in \mathbb{R}^{N\times 1}$, and  $\mathbf{A} \in \mathbb{R}^{M\times N} $ We can see that $f(.)$ is in the form of $\sqrt{1+y^2}$ and is a convex function. It can be also shown that f(.) is bounded in $[\sqrt{2}, 2]$.  This is a convex minimization problem with a linear constraint.Which are the standard algorithms used to solve these kind of problems?Using the specific nature of the problem, is it possible to solve it using any standard optimization software/package?
Maximizing a convex function (minimizing a concave function) with a linear constraint
optimization