semidefinite programming (sdp) forms a class of convex optimization problems with remarkable modeling power. apart from its classical applications in combinatorics and control, it also enjoys a range of applications in data science. this talk first discusses various concrete sdps in data science and their conditioning. in particular, we show that even though slater’s constraint qualification condition may fail, these sdps satisfy an important regularity, strict complementarity, which ensures the good conditioning of the problem. in the second part of the talk, based on the regularity and computational structure shared by these problems, we design time- and space-efficient algorithms to solve these sdps.