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Further fixes
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lauramurgatroyd committed Dec 17, 2024
1 parent 33c90f8 commit f30d864
Showing 1 changed file with 8 additions and 6 deletions.
14 changes: 8 additions & 6 deletions Wrappers/Python/cil/optimisation/algorithms/FISTA.py
Original file line number Diff line number Diff line change
Expand Up @@ -33,13 +33,14 @@ class ISTA(Algorithm):
.. math:: \min_{x} f(x) + g(x)
where :math:`f` is differentiable, :math:`g` has a *simple* proximal operator and :math:`\alpha^{k}`
is the :code:`step_size`.
where :math:`f` is differentiable, and :math:`g` has a *simple* proximal operator.
In each update, the algorithm computes:
.. math:: x_{k+1} = \mathrm{prox}_{\alpha g}(x_{k} - \alpha\nabla f(x_{k}))
where :math:`\alpha` is the :code:`step_size`.
Note
----
Expand Down Expand Up @@ -229,10 +230,9 @@ class FISTA(ISTA):

r"""Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), see :cite:`BeckTeboulle_b`, :cite:`BeckTeboulle_a` is used to solve:
.. math:: \min_{x} f(x) + g(x)
.. math:: \min_{x} f(x) + g(x)
where :math:`f` is differentiable, :math:`g` has a *simple* proximal operator and :math:`\alpha`
is the :code:`step_size`.
where :math:`f` is differentiable and :math:`g` has a *simple* proximal operator.
In each update the algorithm completes the following steps:
Expand All @@ -245,7 +245,9 @@ class FISTA(ISTA):
y_{k+1} = x_{k} + \frac{t_{k}-1}{t_{k+1}}(x_{k} - x_{k-1})
\end{cases}
Note that the above applies for :math:`k\geq 1`. For :math:`k\eq 0` :math:`x_{0}` and :math:`y_{0}` are initialised to `initial`, and :math:`t_{1}=1`
where :math:`\alpha` is the :code:`step_size`.
Note that the above applies for :math:`k\geq 1`. For :math:`k=0` :math:`x_{0}` and :math:`y_{0}` are initialised to `initial`, and :math:`t_{1}=1`
Parameters
Expand Down

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