I'm familiar with linear programs in that they can solve problems with linear objective functions and linear constraints. But what can semidefinite programming solve that linear programming can't? I already know that semidefinite programs are a generalization of linear programs.
Also, how does one recognize a problem that can be solved using semidefinite programming? What is a typical problem that semidefinite programming is used for that couldn't be solved via linear programming?
Thanks very much for any response.