SOCP implementation

I have the simple cone constraint xy >= z^2 and I use CPLEX. As far as I know,
CPLEX can only handle SCP constraints type: x-y^2 .=0. x^2 + y^2 <=t.
Does anybody know how can I implelent the constraint xy >= z^2 in CPLEX?

Jun 27, 4:18*pm, "MichaelCh" <u44519@uwewrote:
I have the simple cone constraint xy >= z^2 and I use CPLEX. As far as I know,
CPLEX can only handle SCP constraints type: x-y^2 .=0. x^2 *+ y^2 <=t.
Does anybody know how can I implelent the constraint xy >= z^2 *in CPLEX?

CPLEX SCP only handles constraints of type: -c0*x0^2 + sum(i,
ci*xi^2) <= 0

remember that (x+y)^2 = x^2 + y^2 +2x*y, so x*y = (x+y)^2/2 - x^2/2 -
y^2/2
then x*y >= z^2 <=(x+y)^2/2 - x^2/2 - y^2/2 >= z^2
define x+y = a
then -a^2/2 + x^2/2 + y^2/2 + z^2 <= 0 is your constraint, as you
wanted.