Solving cubic objective with linear constraints in cvxopt

[Mi Sch]

Dear all,

does anybody know if it is possible to solve a minimization problem with a cubic convex obective function and linear constraints in cvxopt? 

I checked the tutorials at the webpage, but I didn't find an example with a polynomial convex objective. Is it possible to transform it in another kind of problem (SOCP or semidefinite programming)?

The obj looks like the picture that i attached, there only is one more linear constraint in my case.

Thanks!

Best,

Michel

[Joachim Dahl]

That can be solved as an SOCP.  You have to do the reformulation by hand as shown in the book by Ben-Tal and Nemerovski,  or Boyd and Vandenberghe.

You can also use a modeling framework like cvxpy, which makes it alot easier.

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[Mi Sch]

Thank you for the response. I try to find an example where they have polynomial constraints or objective which are not quadratic, but they only have quadratic ones. Do you have an example how to transform a polynomial convex programming into socp? I dont know how to start there.

Am Montag, 14. August 2017 23:20:32 UTC+2 schrieb Joachim Dahl:

That can be solved as an SOCP.  You have to do the reformulation by hand as shown in the book by Ben-Tal and Nemerovski,  or Boyd and Vandenberghe.

You can also use a modeling framework like cvxpy, which makes it alot easier.

On Mon, Aug 14, 2017 at 5:34 PM, 'Mi Sch' via CVXOPT <cvx...@googlegroups.com> wrote:

Dear all,

does anybody know if it is possible to solve a minimization problem with a cubic convex obective function and linear constraints in cvxopt? 

I checked the tutorials at the webpage, but I didn't find an example with a polynomial convex objective. Is it possible to transform it in another kind of problem (SOCP or semidefinite programming)?

The obj looks like the picture that i attached, there only is one more linear constraint in my case.

Thanks!

Best,

Michel

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[Joachim Dahl]

There are similar examples in the MOSEK documentation:

http://docs.mosek.com/modeling-cookbook/cqo.html#conic-quadratic-modeling

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