Question

为什么用LINGO软件求解线性规划和整数规划问题时不会出错，而在求解非线性问题是总是有问题？？？

非线性例1：
MODEL
MAX 86 R+93 U+106 P-78 A1-88 A2-75 T-130 L
2) A < 10000
3) T < 11000
4) L < 6000
5) R > 5000
6) U > 5000
7) P > 5000
8) SA = ( .04 A1 + .01 A2 ) / A
9) OA = ( 91 A1 + 97 A2 ) / A
10) A = A1 + A2
11) P = LP + TP + AP
12) U = TU + AU
13) L = LP + LR
14) A = AP + AU + AR
15) T = TP + TU + TR
16) ( AR OA + 83 TP + 800 LR ) / R > 90
17) ( AP OA + 83 TP + 800 LP ) / P > 94
18) ( AU OA + TU 83 ) / U > 88
19) ( SA AR + .02 TR ) / R < .03
20) ( SA AP + .02 TP ) / P < .028
21) ( SA AU + .02 TU ) / U < .03
22) LP > 0
23) TP > 0
24) AP > 0
25) TU > 0
26) AU > 0
27) LR > 0
28) TR > 0
29) AR > 0
30) R = TR + AR + LR
END
非线性例2：
MIN = 200 *D1 + 150 *D2 + 200 *D3 + 300 *D4
2) D1 =( ( X - 5 ) ^ 2 + ( Y - 10 ) ^ 2 ) ^ .5
3) D2 =((X-10)^2+(Y-5)^2)^.5
4) D3 =(X^2+(Y-12)^2)^.5
5) D4 =((X-12)^2+Y^2)^.5
END

Answer 1

MIN = 200 *D1 + 150 *D2 + 200 *D3 + 300 *D4;
D1 =( ( X - 5 ) ^ 2 + ( Y - 10 ) ^ 2 ) ^ 0.5;
D2 =((X-10)^2+(Y-5)^2)^0.5;
D3 =(X^2+(Y-12)^2)^0.5;
D4 =((X-12)^2+Y^2)^0.5;

运行结果：

Global optimal solution found.
Objective value: 5456.540
Objective bound: 5456.535
Infeasibilities: 0.2220446E-15
Extended solver steps: 140
Total solver iterations: 29710

Variable Value Reduced Cost
D1 6.582233 0.000000
D2 0.6864352 0.000000
D3 11.63411 0.000000
D4 5.701016 0.000000
X 9.314165 0.000000
Y 5.028705 0.2379409E-08

Row Slack or Surplus Dual Price
1 5456.540 -1.000000
2 0.000000 -200.0000
3 0.000000 -150.0000
4 0.000000 -200.0000
5 0.000000 -300.0000