Does the number of quadratic term affect the number of SOCP constraint generated by YALMIP

[JackJack]

Dear Professor Johan 

Given that x-y+z >= 0 and all decision variable x,y,z are non-negative will the number of quadratic term on the left hand side of C1 and C2 affect the number of constraint generated by YALMIP after reformulation.

C1 has 2 quadratic term on the LHS
C2 has 3 quadratic term on the LHS

I know that both C1 and C2 can be reformulate as a single SOCP constraint but assuming that I am using a dumb method like this


The reason I am asking this stupid question is that because in my model sometimes the degree is not quadratic but can become even degree like 4,6,8,10 so we may have cpower() of 4,6,10.

Thank you and best regard

[Johan Löfberg]

cpower with power 2 cannot be on the right side, as it violates convexity propagation rules. Likewise squaring it will (should) not work.

For the quadratic case with the positivity property you should simply state z^z<=u^2 as norm(z)<= u. If you stick to the quadratic form I am not sure YALMIP detects the convex structure (it does some automatic rotatated socp detection but not sure here)

C1 and C2 will have same size as it is a simple quadratic so no modelling is really done (before actually setting up an SOCP for the detected quadratic constraint)