# 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?
• 740
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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 ...
• 558
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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 ...
• 558
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### Is Sum of Absolute Value / ${L}_{1}$ Norm of Differences Convex?

I'm not sure how to approach this exercise. One idea is to derive it w.r.t z, show that there is a min-extremum at $z=f_k$ and then show that for each value from the right and the left of the loss ...
• 175
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### Justification for Squared ${L}_{2}$ Data and Smoothness Term as an Error Bound

Often in variational methods (and not only) we have an energy that is of the form: $$E(u) = \frac{1}{2}\|f-u\|^2_2 + \frac{\alpha}{2}\|\psi(u)\|^2_2,$$ where the first term is referred to as the data ...
• 195
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### Quadratic Programming with Linear Equality Constraints

I need to solve an equality constrained minimization problem as give below $$\min_{\textbf{w}} \mathbf{w}^TR\mathbf{w}$$ such that $$X\mathbf{w} = \mathbf{1}$$ where $R\in \mathbb{R}^{n\times n}$ is ...
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