Proximal gradient method: Difference between revisions

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in that 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 [[smooth function]] among <math>f_1, . . . , f_n</math> is involved via its proximity

operator. Iterative Shrinkage thresholding algorithm, [[Landweber iteration|projected Landweber]], projected<ref>

{{cite news | last1="Daubechies | first1=I | last2=Defrise | first2 = M | last3 = De Mol| first3 = C| title=An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

|journal=A Journal Issued by the Courant Institute of Mathematical Sciences|volume=57 |year=2004|pages=1413-1457}}</ref>, [[Landweber iteration|projected Landweber]], projected

gradient, [[alternating projection]]s, [[Alternating direction method of multipliers#Alternating direction method of multipliers|alternating-direction method of multipliers]], alternating

split [[Bregman method|Bregman]] are special instances of proximal algorithms. Details of proximal methods are discussed in Combettes and Pesquet.<ref>