Proximal gradient method: Difference between revisions

Revision as of 17:45, 26 December 2024

Revision as of 12:23, 21 June 2025

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<math>

\operatorname{min}\limits_min_{x \in \mathbb{R}^Nd} \sum_{i=1}^n f_i(x)

</math>

where <math>f_i: \mathbb{R}^Nd \rightarrow \mathbb{R},\ i = 1, \dots, n</math> are possibly non-differentiable [[convex functions]]. The lack of differentiability rules out conventional smooth optimization techniques like the [[Gradient descent|steepest descent method]] and the [[conjugate gradient method]], but proximal gradient methods can be used instead.

Proximal gradient methods starts by a splitting step, in which the functions <math>f_1, . . . , f_n</math> are used individually so as to yield an easily [[wikt:implementable|implementable]] algorithm. They are called [[proximal]] because each non-differentiable function among <math>f_1, . . . , f_n</math> is involved via its [[Proximal operator|proximity operator]]. Iterative shrinkage thresholding algorithm,<ref>