# Questions tagged [convex-optimization]

The tag has no usage guidance.

47 questions
Filter by
Sorted by
Tagged with
1 vote
86 views

36 views

### Image Restoration and Standard Forms of Second Order Cone Programming (SOCP)

I'm studying the application of SOCP methods in Image restoration And I want to understand the difference between the two formulas of SOCP and how they are related. Standard form (1) : min $f^{t}x$ ...
265 views

### Solving LASSO (Basis Pursuit Denoising Form) with LARS

I'm now working on using LARS (Least Angle Regression) algorithm to solve a LASSO problem in Basis Pursuit Denoising form like: \begin{align*} \quad && \arg \min_{\beta}{\left\| y - X\beta \...
168 views

### On the Use of OMP Algorithm to Estimate Sparse Vector

As known, Orthogonal Matching Pursuit (OMP) Algorithm is to recover the sparse channel after convolution with another vector. But when I implement that in MATLAB, I don't get the sparse vector ...
207 views

### How to solve ADMM for TV Minimization Problem For Different Sizes $A$ and $x$ in $Ax=b$

I have matrix $A$ that is $(M \times M)$ square matrix, $x$ $(M \times N)$ matrix, $b$ is $(M \times N)$ matrix. Knowing $A$ and $b$ I would like to get the $x$ from the equation $Ax=b$. $N=p \times q$...
25 views

### Solving Sparse Model with given Dictionary Using LASSO

I was trying to solve a problem where the basis matrix contains the components of $\sin(nx)$, $\cos(nx)$, $\sinh(nx)$ and $\cosh(nx)$. Say the $n$ varies from 1 to 100. While solving the lasso linear ...
438 views

### Proximal Gradient Method (PGM) for a Function Model with More than 2 Functions (Sum of Functions)

I am currently working in signal reconstruction. I am trying to develop an algorithm where the user can plug any constraint to the main objective function (let's say chi2, least squares). I was trying ...
35 views

### Rakeness Optimization problem

Rakeness optimization problem demonstrate that increases the rakeness between $a$ , $b$ while leaving $b$ random enough. where $e$ is the energy of the projection waveforms and $r$ is a randomness-...
134 views

### Convex Optimization with ${L}_{1, 2}$ Regularization Term

I have an optimization problem such as follow: $$\underset{X}{\operatorname{argmin}}\sum _s \left \| T_sX_{:,s} - Y_{:,s} \right \|^2_2 +\lambda\left \| GX \right \|_{2,1} \tag{1}$$ I have introduced ...
146 views

### Why Does FISTA Algorithm Not Work for Signed Signals?

Using the FISTA Algorithm for compressive sensing from Tiep H. Vu - FISTA, I created the matlab example below. I created 2 sparse signals x_signed and x_pos, where the latter only contains positive ...
153 views

### Resources on Solving Convex Optimization Problems in the Compressed Sensing Field

When I read papers of compressed sensing, sparse representation and whatever requiring optimization of a cost function, I just find the final results as an iterative equation or so which will converge ...
304 views

### Constrained LASSO Problem - ${L}_{1}$ Regularized Least Squares with Linear Equality Constraints

I have an optimization question. I want to solve the following problem: $$\arg\min_S\frac{1}{2}\|s-c\|_2^2 +\lambda\|\Phi s\|_1 \mbox{ s.t. } As = 0$$ in which $\Phi$ is the wavelet transform ...
55 views

### Wireless Body Area Networks with Minimum Energy Consumption [closed]

For adaptive compressive sensing(cs),the sensing matrix is related to the input signal. For example, in rakeness-based(cs), the sensing matrix is obtained by solving an optimization problem which ...
1 vote
474 views

### Fast Optimization for Long FIR Filters

I need FIR filter lengths in the order of 1e4 and above to obtain reasonable accuracy in desired frequency response. The problem is that optimisation in MATLAB (e.g. fircls or the Optimization Toolbox)...