Iterative soft-thresholding algorithm
= Iterative soft-thresholding algorithm
= ISTA
{c}
{synonym}
The iterative soft-thresholding algorithm applies the <proximal gradient method> to $\|x\|_1+\tfrac12\|Ax-y\|_2^2$:
$$
x^{k+1}=S_\tau(x^k-\tau A^T(Ax^k-y)),\qquad0<\tau\le\|A\|_{2\to2}^{-2}.
$$
Here $S_\tau$ is coordinatewise <soft thresholding>. The objective is <convex> and coercive, so iterates converge to a minimizer in finite dimensions; uniqueness requires additional hypotheses.