As part of a research project I'm supposed to write an semidefinite programming solver in Matlab (similar to SDTP3, MOSEK, SEDUM, etc) except it needs to be able to solve to many significant digits accurately, where many of these solvers may only have ~3 or 4 significant digits.
I have essentially no experience with SDP/LMI's, and was wondering what the best way to go about learning a bit about this would be, and if anyone has any ideas for what might be the best algorithms and methods to use to build this? I'm at a bit of a loss after looking into it for a while and would appreciate any suggestions.
Thank you so much for all your time!