[documentation] Add a tutorial for LBFGS #404
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amontoison
reviewed
Jan 27, 2025
amontoison
reviewed
Jan 27, 2025
| Hence, the problem is good candidate for a quasi-Newton algorithm. | ||
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| We start by solving the problem with the default options in MadNLP, | ||
| using the dense linear solver Lapack: |
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| using the dense linear solver Lapack: | |
| using a dense linear solver from LAPACK: |
amontoison
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amontoison
reviewed
Jan 28, 2025
| ``` | ||
| with ``\xi > 0`` a scaling factor, ``U_k`` and ``V_k`` two ``n \times 2p`` matrices. | ||
| The number ``p`` denotes the number of vectors used when computing the limited memory updates | ||
| (the parameter ``max_history`` in MadNLP): the larger, the more accurate is the low-rank approximation. |
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| (the parameter ``max_history`` in MadNLP): the larger, the more accurate is the low-rank approximation. | |
| (the parameter `max_history` in MadNLP): the larger, the more accurate is the low-rank approximation. |
blegat
reviewed
Jan 28, 2025
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| !!! info | ||
| As MadNLP is designed to solve constrained optimization problems, | ||
| it does not approximate the inverse of the Hessian matrix, as it is done |
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| it does not approximate the inverse of the Hessian matrix, as it is done | |
| it does not approximate the inverse of the Hessian matrix, as done |
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cc @amontoison @blegat
Solve #400