Question

用lingo求解非线性规划问题，为何解不出来

model:
min=x1+x2+x3;
x1*r11+x2*r12+x3*r13>=50;
x1*r21+x2*r22+x3*r23>=20;
x1*r31+x2*r32+x3*r33>=12;
x1*r41+x2*r42+x3*r43>=15;
4*r11+5*r21+6*r31+7*r41<=17;
4*r12+5*r22+6*r32+7*r42<=17;
4*r13+5*r23+6*r33+7*r43<=17;
4*r11+5*r21+6*r31+7*r41>=14;
4*r12+5*r22+6*r32+7*r42>=14;
4*r13+5*r23+6*r33+7*r43>=14;
x1+x2+x3>=29;
x1+x2+x3<=33;
x1>=x2;
x2>=x3;
@gin(x1);@gin(x2);@gin(x3);
@gin(r11);@gin(r12);@gin(r13);
@gin(r21);@gin(r22);@gin(r23);
@gin(r31);@gin(r32);@gin(r33);
@gin(r41);@gin(r42);@gin(r43);
end

Answer 1

model:
min=x1+x2+x3;
x1*r11+x2*r12+x3*r13>=50;
x1*r21+x2*r22+x3*r23>=20;
x1*r31+x2*r32+x3*r33>=12;
x1*r41+x2*r42+x3*r43>=15;
4*r11+5*r21+6*r31+7*r41<=17;
4*r12+5*r22+6*r32+7*r42<=17;
4*r13+5*r23+6*r33+7*r43<=17;
4*r11+5*r21+6*r31+7*r41>=14;
4*r12+5*r22+6*r32+7*r42>=14;
4*r13+5*r23+6*r33+7*r43>=14;
x1+x2+x3>=29;
x1+x2+x3<=33;
x1>=x2;
x2>=x3;
@gin(x1);@gin(x2);@gin(x3);
@gin(r11);@gin(r12);@gin(r13);
@gin(r21);@gin(r22);@gin(r23);
@gin(r31);@gin(r32);@gin(r33);
@gin(r41);@gin(r42);@gin(r43);
end

求解结果如下：
Global optimal solution found.
Objective value: 29.00000
Objective bound: 29.00000
Infeasibilities: 0.000000
Extended solver steps: 1
Total solver iterations: 9742

Variable Value Reduced Cost
X1 14.00000 0.000000
X2 12.00000 0.000000
X3 3.000000 0.000000
R11 3.000000 0.000000
R12 1.000000 0.000000
R13 0.000000 0.000000
R21 1.000000 0.000000
R22 0.000000 0.000000
R23 2.000000 0.000000
R31 0.000000 0.000000
R32 1.000000 0.000000
R33 0.000000 0.000000
R41 0.000000 0.000000
R42 1.000000 0.000000
R43 1.000000 0.000000