Frank–Wolfe algorithm: Difference between revisions

Revision as of 18:10, 16 December 2014

Revision as of 18:19, 16 December 2014

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==Algorithm==

[[File:Frank-Wolfe Algorithm.png|thumbnail|right|A step of the Frank-WolfeFrank–Wolfe algorithm]]

:''Initialization:'' Let <math>k \leftarrow 0</math>, and let <math>\mathbf{x}_0 \!</math> be any point in <math>\mathcal{D}</math>.

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</math>

The latter optimization problem is solved in every iteration of the Frank-WolfeFrank–Wolfe algorithm, therefore the solution <math>\mathbf{s}_k</math> of the direction-finding subproblem of the <math>k</math>-th iteration can be used to determine increasing lower bounds <math>l_k</math> during each iteration by setting <math>l_0 = - \infty</math> and

:<math>

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==Bibliography==

*{{cite journal|last=Jaggi|first=Martin|title=Revisiting Frank-WolfeFrank–Wolfe: Projection-Free Sparse Convex Optimization|journal=Journal of Machine Learning Research: Workshop and Conference Proceedings |volume=28|issue=1|pages=427–435|year= 2013 |url=http://jmlr.csail.mit.edu/proceedings/papers/v28/jaggi13.html}} (Overview paper)

*[http://www.math.chalmers.se/Math/Grundutb/CTH/tma946/0203/fw_eng.pdf The Frank-WolfeFrank–Wolfe algorithm] description

==External links==

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== See also ==

* [[Proximal Gradientgradient Methodsmethods]]

{{Optimization algorithms|convex}}