Survey on Optimization algorithms
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