Simple SOCP socp Gurobi AMPL short = 0; var z >= 0; maximize obj: x; subject to sonc1: x + y + z = 1; # need z >= 0 to convey SOC subject to sonc2: x^2 + y^2 <= z^2; # need y,z >= 0 to convey rotated SOC subject to sonc3: x^2 <= y*z; solve; ]]> Problem given in Gurobi website