Abstract
Conic optimization includes some of the most well-known convex optimization problems, all of which require the variables to be inside a specific convex cone. Many recent progress in conic programming comes from improving the cost per iteration by designing faster dynamic data structures. In this talk I will cover some recent results of faster algorithms for linear programming (LP), semidefinite programming (SDP), and sum-of-squares (SOS) optimization using faster inverse maintenance data structures, where each data structure exploits the special structures of the optimization problem itself.