Simple SOCP
socp
FICO-Xpress
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;
]]>
Simple SOCP