# Questions tagged [convex-optimization]

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### How Could One Accelerate the Convergence of the Least Mean Squares (LMS) Filter?

How can the convergence of an LMS filter be accelerated? Can we do better than the vanilla algorithm?
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### Converting Hadamard Product into Matrix Multiplication in Image Deconvolution with Total Variation (TV) Using ADMM

I would like to solve the following Image Deconvolution equation by ADMM. $$\mathbf { \min\frac{1}{2}\Vert{Cx-b}\Vert_2^2+\Vert w\circ (D x)\Vert_1 \tag 1}$$ Where, $x$ is a vector of unknown pixel ...
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### Optimization of square matrix multiplied with another matrix to have the final result a unitary matrix

I have a square matrix $D$ whose size is $m \times m$ multiplied with another $m \times m$ square matrix $C$, I need to optimize the matrix $C$ to have a unitary matrix $DC$. I mean optimize the ...
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### What are some reliable sources which I can use to validate my code for simulating MPC?

What I have done I have written a code in Mathematica from scratch for simulating quadratic cost standard MPC problems for constant reference tracking. My attempts YALMIP's website has a solved ...
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### time-domain channel estimation based on two vectors optimization

Let's the input data vector $X = [X_1, X_2, X_3, X_4, X_5,X_6,X_7,X_8];$ where $[X_7,X_8]$ are well known, and the vector $y = h*X$ where $*$ is the convolution operation and $h = [h_1,h_2]$ is the ...
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### Automatic Image Enhancement of Images of Scanned Documents (Auto Whitening)

Dropbox have make a blog post about there automatic enhancement method for scanned document image - Fast Document Rectification and Enhancement. I followed the post and they mention a formula to make ...
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### Solving LASSO (${L}_{1}$ Regularized Least Squares) with Gradient Descent

To the best of my knowledge, state of the art methods for optimizing the LASSO objective function include the LARS algorithm and proximal gradient methods. I was wondering however, if the LASSO ...
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### Difference Between Iteratively Reweighted Least Squares (IRLS) and Sequential Quadratic Programming?

Part of my work is concerned with applications in Sparse Bayesian Learning and therefore I occasionally stumble over interesting papers in the field of compressed sensing. I recently read ...
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### Understanding Soft Thresholding Operator

I want to understand what is soft thresholding operator? Why we use this operator? I came across this term while I was reading the paper - A New Algorithm Based on Linearized Bregman Iteration with ...
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### How Come RIP Guarantees Unique Restoration of the Sparse Solution by ${L}_{1}$ Minimization?

We have a sensing matrix $\Phi$, satisfying the restricted isometry property (RIP), and a sparse signal $x$. We want to recover $\hat x$ from the measurement $y=\Phi x$ by using $l_1$-minimization. I ...
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The quadratic performance surface of an adaptive filter is a paraboloid. Its minimum can be found wherever the gradient is zero. However, since there are two types of paraboloids (elliptical and ...
Consider the cost function $$f(X,\lambda) = \|AX-b\|_2^2 + \alpha \|LX\|_2^2$$ $A:$Measurement matrix($R_{m\times n}$,$m \ll n$), $b:$observation vector($R_m$), $L:$Laplacian operator($R_{n \times n}... 2answers 612 views ### Significance of$ \lambda $in Basis Pursuit In basis Pursuit, L1 minimization is done to perform compressed sensing. In the literature there is a$ \lambda $parameter used as a regularizer. What is its significance? 1answer 270 views ### Least Angle Regression (LARS) without Matrix Inversion Sorry if this is too damned long. I did what I could to abbreviate it. The question is about Least Angle Regression (LARS). I'm new to numerical work with matrices. I believe I have a way to ... 1answer 149 views ### Ideas on Matrix Factorization / Transformations for$ {L}_{1} $Minimization I am starting with a typical$\ell_1$basis pursuit problem: $$\min_{\mathbf{x}} \Vert \mathbf{x} \Vert_1 \quad \mathrm{s.t.} \quad \Vert \mathbf{ERx} - \mathbf{y} \Vert_2 \leq \epsilon,$$ where$\...
The highest voted answer to this question suggests that to denoise a signal while preserving sharp transitions one should minimize the objective function: $$|x-y|^2 + b|f(y)|$$ where \$...