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More Is there a class of optimization problems more general than semidefinite programprogramming?

I was TAingTA-ing my convex optimization class and explaining that Linear Programslinear programs are a special case of Second Order Cone Programssecond-order cone programs, which are themselves special cases of Semidefinite Programssemidefinite programs. My question is, isIs there any well-established class of optimization problems that is more general than semidefinite programs?  Conic optimization problems would be an example of this, but I'm hoping for something a little more algebraic, if it exists.

More general than semidefinite program?

I was TAing my convex optimization class and explaining that Linear Programs are a special case of Second Order Cone Programs, which are themselves special cases of Semidefinite Programs. My question is, is there any well-established class of optimization problems that is more general than semidefinite programs?  Conic optimization problems would be an example of this, but I'm hoping for something a little more algebraic, if it exists.

Is there a class of optimization problems more general than semidefinite programming?

I was TA-ing my convex optimization class and explaining that linear programs are a special case of second-order cone programs, which are themselves special cases of semidefinite programs. Is there any well-established class of optimization problems that is more general than semidefinite programs? Conic optimization problems would be an example of this, but I'm hoping for something a little more algebraic, if it exists.

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More general than semidefinite program?

I was TAing my convex optimization class and explaining that Linear Programs are a special case of Second Order Cone Programs, which are themselves special cases of Semidefinite Programs. My question is, is there any well-established class of optimization problems that is more general than semidefinite programs? Conic optimization problems would be an example of this, but I'm hoping for something a little more algebraic, if it exists.