Theoretical Computer Science Stack Exchange is a question and answer site for theoretical computer scientists and researchers in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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 Computer Science which has a broader scope. – Kaveh Dec 24 '12 at 21:37
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 Dec 24 '12 at 21:39

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.