Practical applications of semidefinite programming

I am looking for practical applications of semidefinite- programming. So far, I found that the low-rank matrix completion problem (recomendendattion matrices) can be expressed as a semidefinite program. The same goes for the combinatorial problem MAX-CUT.

1. What is a practical applications of the MAX-CUT problem?
2. What would be a third practical applications of semidefinite programming?

Would be nice if anyone could recommend any references. Thanks.

• Do they use semidefinite programming in industry? – Rodrigo de Azevedo Apr 2 at 6:49
• One application is determining whether a polynomial can be expressed as a sum of squares. Take a look at this. – Rodrigo de Azevedo Apr 2 at 6:51
• If you haven't already read Boyd and Vandenberghe, it discusses a bunch of applications of SDPs (including in the exercises and the additional exercises). – littleO Apr 2 at 9:19
• I've looked into Boyd and Vandenberghe. Problem is, these problems are convex or quasiconvex and since semidef. problems are just a subfield, things dont really fit. Or am I wrong here? – P.Müller Apr 3 at 4:12
• @Rodrigo the sum of squares is quite interesting. I read math.stackexchange.com/questions/2410994/… . How would I have to choose A_i if I want to transform min tr(Q) s.t. A(Q)=b,Q⪰O to the standard sdp form min tr(C,Q) s.t. Q⪰O ,tr(A_i,Q)=b_i . – P.Müller Apr 3 at 4:49