Dear Johan,
The gurobi version 5.6 claims that it is capable of solving quadratically constrained problems (including MI type), and YALMIP recognizes quadratic constraints, however, when I try to use solvesdp with quadratic constraints and gurobi as a solver, it reports "Warning: Solver not applicable (gurobi)":
>> x=sdpvar(2,1);
f=x(1)^2+x(2)^2<=4;
f=f+(x(:)>=0);
solvesdp(f,-x(1)-x(2),sdpsettings('solver','gurobi'))
[-1 -1]*double(x(:))
Warning: Solver not applicable (gurobi)
ans =
solvertime: 0
info: 'Solver not applicable (gurobi)'
problem: -4
yalmiptime: 0.3138
CPLEX, however, recognizes it as QCP and solves it correctly...
I tried looking for the differences in solver settings via definesolvers function, but they seem to have the same values regarding supported types of inequalities.
I am using gurobi-mex 1.61, MATLAB R2012a and YALMIP 20130628.