benchopt / benchopt/benchmark_tv_1d

Norm of DA_inv of DPGD

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Dominant language
Python
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2
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Description

In the algorithm Dual proximal gradient descent, we need $\ || DA^{\dagger} \ ||_2^2$ to calculate stepsize.

When $A$ is a matrix, it's possible to get $A^{\dagger}$ by ```np.linalg.pinv```, but when $A$ is an linear operator, it's difficult to get its inverse. $A$ could be an operation of convolution, and it could also be a mutiplication by a matrix.

We have tried to approximate it
- by $\frac{1}{\|| AD^{\dagger} \||_2^2}$, but it turned out its not the same value for every case;
- by ```np.fft.fft```, but it didn't work neither.

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Research direction

No file or test is named in the issue. Start by locating the Dual proximal gradient descent implementation and the code that computes the stepsize, then inspect how matrix and linear-operator cases are represented. Done means obtaining a correct value for ||DA†||₂² for both matrix and convolution operators, with comparisons against the available pinv-based matrix case and representative tests.

Written by the indexing model from the issue text.

Assessment

Tech stack
numpy, python
Domain
backend
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
25/100

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