var x{1..4} := 1;

minimize f:
	x[1]*x[2];
subject to cons1:
	(x[1]*x[3]+x[2]*x[4])^2/(x[1]^2+x[2]^2) - x[3]^2 - x[4]^2 +
	1= 0;
subject to cons2:
	x[1]-x[3]-1 >= 0;
subject to cons3:
	x[2]-x[4]-1 >= 0;
subject to cons4:
	x[3]-x[4] >= 0;
subject to cons5:
	x[4] >= 1;

solve;
display f;
display x;