1
vote
1answer
30 views

linearization of $\log(|x|)$

I am trying to convexify $\log(|x|)$. I think its concave. So I am trying to get an affine upper bound through linearization. But the problem is there are two concave functions because of the absolute ...
2
votes
0answers
29 views

Monotononically Increasing Water Filling Solution?

$\mathbf{I}$ is the $K\times K$ identity matrix. $\mathbf{h}_i\in\mathbb{C}^{M\times1}\quad\forall1\leq i\leq K$ are column vectors. Consider the solution of the convex optimisation problem over ...
0
votes
1answer
35 views

Effect of Moving within the Feasible Region

$f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a concave function with local maximum at $\mathbf{x}^*$ in a convex, closed feasible set $\mathcal{F}\subset\mathbb{R}^n$. Now consider a suboptimal point ...
3
votes
1answer
197 views

Fitting Shape in Circle for Shape Classification

I need to classify arbitrary 2D shapes. The classification should be invariant to at least affine transform. To achieve this invariance, I decided to "normalize" each shape by fitting it to a unit ...
1
vote
1answer
271 views

Minimising a matrix equation to find 'best fit' affine matrix

Here is my problem: I have an image divided into segments. Each segment consists of pixels with coordinates (x,y) called vector $v$, each pixel has a length 3 vector RGB called $I(v)$. I want to ...