<p>The problem is
$$\max  f(\mathbf{x}) \text{ subject to } \mathbf{Ax} = \mathbf{b}$$</p>

<p>where $f(\mathbf{x}) = \sum_{i=1}^N\sqrt{1+\frac{x_i^4}{(\sum_{i=1}^{N}x_i^2)^2}}$, <br/>
$\mathbf{x} = [x_1,x_2,...,x_N]^T \in \mathbb{R}^{N\times 1}$, and  <br/>
$\mathbf{A} \in \mathbb{R}^{M\times N} $ <br/></p>

<p>$f(.)$ is in the form of $\sqrt{1+y^2}$. Hence <em>f</em>(.) is a convex function.
which is bounded in $[\sqrt{2}, 2]$. <br/> </p>

<p>I am looking for efficient algorithms which solve the above problem or convex maximization problem, in general.</p>

<p>Also, is it possible to solve the above problem using standard convex optimization tools by putting more constraints? </p>

CC BY-SA 3.0
2012-12-24T21:37:58.390Z
Welcome to cstheory, a Q&A site for *research-level* questions in *theoretical computer science* (TCS). Your question does not appear to be a research-level question in TCS. Please see the [FAQ] for more information on what is meant by this. Your question might be suitable for [cs.se] which has a broader scope.
Kaveh
CC BY-SA 3.0
2012-12-24T21:39:28.877Z
ps: the question might be fine here if you edit it so it is not as localized, e.g. you can ask more generally about efficient algorithms for solving classes of convex maximization problems.
Kaveh
<ds.algorithms><convex-optimization>
Maximizing a convex function with linear constraint
Sooraj
# Maximizing a convex function with linear constraint

(Asked by: username_0 on 2012-12-24)

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?

**Tags:** ds.algorithms, convex-optimization
> **Comments:**
> **username_1**: Welcome to cstheory, a Q&A site for *research-level* questions in *theoretical computer science* (TCS). Your question does not appear to be a research-level question in TCS. Please see the [FAQ] for more information on what is meant by this. Your question might be suitable for [cs.se] which has a broader scope.  
> **username_1**: ps: the question might be fine here if you edit it so it is not as localized, e.g. you can ask more generally about efficient algorithms for solving classes of convex maximization problems.  

---

## 0 answers

