Projections onto convex sets: Difference between revisions

Revision as of 21:40, 8 September 2017

Revision as of 21:41, 8 September 2017

Line 51:

Since <math> x_{k+1} = y_{k+1} </math> and assuming <math> x_0 = y_0 </math>, then <math>x_j=y_j</math> for all <math> j \ge 0</math>, and hence we can simplify the iteration to <math> x_{k+1} = \frac{1}{2}( \mathcal{P}_C(x_k) + \mathcal{P}_D(x_k) ) </math>.

== References ==

{{reflist}}

<references>

<ref name="SIAMreview">{{cite journal | last1 = Bauschke | first1 = H.H. | last2 = Borwein | first2 = J.M. | year = 1996 | title = On projection algorithms for solving convex feasibility problems | doi = 10.1137/S0036144593251710 | journal = SIAM Review | volume = 38 | issue = 3| pages = 367–426 }}</ref>

</references>

== Further reading ==

* Book from 2011: [http://www.ec-securehost.com/SIAM/FA08.html Alternating Projection Methods] by René Escalante and Marcos Raydan (2011), published by SIAM.

<ref* The review article from 1996: name="SIAMreview">{{cite journal | last1 = Bauschke | first1 = H.H. | last2 = Borwein | first2 = J.M. | year = 1996 | title = On projection algorithms for solving convex feasibility problems | doi = 10.1137/S0036144593251710 | journal = SIAM Review | volume = 38 | issue = 3| pages = 367–426 }}</ref>

* The review article from 1996:<ref name="SIAMreview" />

[[Category:Convex geometry]]