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This looks like a situation where the Kaczmarz method could work. What you do to maintain an approximate solution and then project cyclically onto the hyperplanes which are given by the $k$-th equati …

I can confirm that there is no agreement of what "extragradient method" really means. I know the interpretation by Christian Clason but I also know the one that is linked in Carlo Beenakkers answer. L …

Evaluation out of bounds is related to boundary conditions. Doesn't the boundary treatment for $C$ already indicate a way to handle the coefficients? If not, I would use some way that extends the coef …

A bit long for a comment. Let's clean up the formulation a bit: First, the domain $[-1,1]^2$ of definition does play any role, and hence, we assume that all respective quantities are functions on s …

Yes, there are. First note that the Wasserstein metric is, after discretization, the solution of a linear program (LP) that can be fed into any LP solver. Moreover, there are specialized algorithms, …

It makes a considerable difference if you need to project a vector just once or repeatedly inside some loop of another algorithm. If you would be in the latter case than it would be indeed a good idea …

You face the curse of dimensionality. Besides the pretty old but simple and robust Monte Carlo integration and its relatives there are also methods based on sparse grids. For an overview see E. No …

Following the suggestion of András Bátkai I post my comment as an answer: Smoothing the dual or the primal problem are quite different things: Smoothing the dual will not give you a smooth primal. Ho …

Not an answer but too many equations for a comment: $\newcommand{\vec}{\mathrm{vec}}$ To compute an element $v\in\mathbb{R}^{3n^2}$ of the kernel of $$M = \begin{bmatrix} A\otimes I\\\\ I\otimes B\en …

The claim in the paper is false. Since the problem is not convex, the claim does not follow from general results. However, there are some results in this direction in quite general cases: If $x^*$ i …

Certainly, there is not a standard method - and be aware that the calculation will be sensitive to noise. A straightforward of calculating the gradient would be: Take some point $x$ and choose a numb …

You have discovered the alias effect! For the discrete Fourier transform all this is worked out in detail - for the discrete Hartley transform, I don't know...

The optimization problem for $f_3$ is $$ \min_g \int_{-1}^1 |g''(x)|^2dx \quad \text{s.t.}\quad \int_{-1}^1 g(x)dx = 0,\ \int_{-1}^1 x g(x)dx = 0,\ \int_{-1}^1 |g(x)|^2dx = 1. $$ Using Lagrange Multip …

I am not aware of results on the linear rate of this variant of the proximal point method. Let me note that convergence is usually shown by the following observation: Since $C$ is a bijection, you may …

Sorry, not an answer, but too long for a comment. If your question is motivated by practical applications of the Radon transform such as computerized tomography in medical imaging or non-destructive …