Proximal gradient method: Difference between revisions

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== Introduction ==

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[http://en.wikipedia.org/wiki/Convex_optimization Convex Optimization] is a sub field of Optimization which can produce reliable solutions

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operator. Iterative Shrinkage thresholding algorithm, [http://en.wikipedia.org/wiki/Landweber_iteration projected Landweber], projected

gradient, [http://en.wikipedia.org/wiki/Alternating_projection alternating projections], [http://en.wikipedia.org/wiki/Alternating_direction_method_of_multipliers#Alternating_direction_method_of_multipliers alternating-direction method of multipliers], alternating

split Bregman are special instances of proximal algorithms. Details of proximal methods are discussed in <ref>

{{cite articlenews |last1=Combettes |first1=Patrick L. |last2= Pesquet |first2=Jean-Chritophe |title=Proximal Splitting Methods in Signal Processing|page={11–23} |year=2009 |url=http://arxiv.org/abs/0912.3522}}</ref>

Methods in Signal Processing|page={11-23} |year=2009 |url=http://arxiv.org/abs/0912.3522}}</ref>

== Notations and Terminology ==

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are required to tackle them. Among the various generalizations of the notion of a convex projection

operator that exist, proximity operators are best suited for other purposes.

== Definition ==

Proximity operators of function <math>f</math> at <math>x</math> is defined as

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*[http://en.wikipedia.org/wiki/Alternating_direction_method_of_multipliers#Alternating_direction_method_of_multipliers Alternating-direction method of multipliers]

*Fast Iterative Shrinkage Thresholding Algorithm (FISTA)<ref>

{{cite articlenews | last1="Beck | first1=A | last2=Teboulle | first2 = M | title=A fast iterative shrinkage-thresholding algorithm for linear inverse problems

|journal=SIAM J. Imaging Science|volume=2 |year=2009|pages=183-202183–202}}</ref>

== Also See also ==

* [http://en.wikipedia.org/wiki/Convex_optimization Convex Optimization]

* [http://en.wikipedia.org/wiki/Alternating_projection Alternating Projection]

== References ==

* {{cite book

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| volume = 49

| year = 2011

| pages = 185-212185–212

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== Notes ==

<references/>

== Also See ==

* [http://en.wikipedia.org/wiki/Convex_optimization Convex Optimization]

* [http://en.wikipedia.org/wiki/Alternating_projection Alternating Projection]

==External links==

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* [http://www.stanford.edu/class/ee364a/ EE364a: Convex Optimization I] and [http://www.stanford.edu/class/ee364b/ EE364b: Convex Optimization II], Stanford course homepages

* [http://www.eecs.berkeley.edu/~elghaoui/Teaching/EE227A/lecture18.pdf‎ EE227A: Lieven Vandenberghe Notes] Lecture 18

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