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Practical applications of semidefinite programming

2

1

$begingroup$

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.

reference-request optimization convex-optimization applications semidefinite-programming

share|cite|improve this question

edited Apr 2 at 6:48

Rodrigo de Azevedo

13.2k41961

asked Apr 1 at 18:07

P.MüllerP.Müller

111

$endgroup$

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  Do they use semidefinite programming in industry?
  $endgroup$
  – Rodrigo de Azevedo
  Apr 2 at 6:49
  

  
  
  
  


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  One application is determining whether a polynomial can be expressed as a sum of squares. Take a look at this.
  $endgroup$
  – Rodrigo de Azevedo
  Apr 2 at 6:51
  
  

  
  
  
  


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  $begingroup$
  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).
  $endgroup$
  – littleO
  Apr 2 at 9:19
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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?
  $endgroup$
  – P.Müller
  Apr 3 at 4:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @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 .
  $endgroup$
  – P.Müller
  Apr 3 at 4:49
  
  

  
  
  
  

 | 
show 2 more comments

2

1

$begingroup$

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.

reference-request optimization convex-optimization applications semidefinite-programming

share|cite|improve this question

edited Apr 2 at 6:48

Rodrigo de Azevedo

13.2k41961

asked Apr 1 at 18:07

P.MüllerP.Müller

111

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Do they use semidefinite programming in industry?
  $endgroup$
  – Rodrigo de Azevedo
  Apr 2 at 6:49
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  One application is determining whether a polynomial can be expressed as a sum of squares. Take a look at this.
  $endgroup$
  – Rodrigo de Azevedo
  Apr 2 at 6:51
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  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).
  $endgroup$
  – littleO
  Apr 2 at 9:19
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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?
  $endgroup$
  – P.Müller
  Apr 3 at 4:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @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 .
  $endgroup$
  – P.Müller
  Apr 3 at 4:49
  
  

  
  
  
  

 | 
show 2 more comments

$begingroup$

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.

reference-request optimization convex-optimization applications semidefinite-programming

share|cite|improve this question

edited Apr 2 at 6:48

Rodrigo de Azevedo

13.2k41961

asked Apr 1 at 18:07

P.MüllerP.Müller

111

$endgroup$

share|cite|improve this question

edited Apr 2 at 6:48

Rodrigo de Azevedo

13.2k41961

asked Apr 1 at 18:07

P.MüllerP.Müller

111

share|cite|improve this question

edited Apr 2 at 6:48

Rodrigo de Azevedo

13.2k41961

asked Apr 1 at 18:07

P.MüllerP.Müller

111

edited Apr 2 at 6:48

Rodrigo de Azevedo

13.2k41961

edited Apr 2 at 6:48

Rodrigo de Azevedo

13.2k41961

asked Apr 1 at 18:07

P.MüllerP.Müller

111

asked Apr 1 at 18:07

P.MüllerP.Müller

111