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I am trying to solve an optimization problem. I need some help in getting the results or survey on related issues. The question is a bit general but any help in identifying the correct sources would help.

Are their any good survey work/tutorial/book that could provide information on the known algorithms and complexity results for $L_{0}$, $L_{1}$, $L_{2}$ optimization and also the relation among them for both sparse and general solutions?

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    $\begingroup$ I would suggest asking for surveys/references in place of results/algorithms, IMHO in the current form the question is too broad. $\endgroup$ – Kaveh Mar 23 '11 at 17:08
  • $\begingroup$ clearly one part of your question relates to compressed sensing, which relates to the $L_1, L_0$ connection $\endgroup$ – Suresh Venkat Mar 23 '11 at 18:35
  • $\begingroup$ @Suresh Venkat - Is it related to Donoho's work? $\endgroup$ – T.... Mar 23 '11 at 21:16
  • $\begingroup$ Yes, and many others as well $\endgroup$ – Suresh Venkat Mar 23 '11 at 22:21
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You will find lots of links in Steve Wright's plenary talk at the SIAM Optimization 2011 conference: http://pages.cs.wisc.edu/~swright/talks/sjw-siopt11.pdf

At the same conference, Michael Friedlander gave a tutorial with many references and pointers to applications and software: http://www.cs.ubc.ca/~mpf/papers/mpf-tutorial-siopt11.pdf

The video lectures on compressive sensing given by Emmanuel Candes at Cambridge are also a great way to get into the subject: http://www.sms.cam.ac.uk/collection/1117766

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