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} $
$f(.)$ is in the form of $\sqrt{1+y^2}$. Hence f(.) is a convex function.
which is bounded in $[\sqrt{2}, 2]$.
I am looking for efficient algorithms which solve the above problem or convex maximization problem, in general.
Also, is it possible to solve the above problem using standard convex optimization tools by putting more constraints?
