Question

用lingo怎么解含参非线性方程

min m
@cos(x1)+@cos(x2)+@cos(x3)=3.14/4*3*m;
@cos(5x1)+@cos(5x2)+@cos(5x3)=0;
@cos(7x1)+@cos(7x2)+@cos(7x3)=0;
@free(x1);
@free(x2);
@free(x3);

怎么用lingo实现
解出的还可以加分

Answer 1

min=m;
@cos(x1)+@cos(x2)+@cos(x3)=3.14/4*3*m;
@cos(5*x1)+@cos(5*x2)+@cos(5*x3)=0;
@cos(7*x1)+@cos(7*x2)+@cos(7*x3)=0;
@free(x1);
@free(x2);
@free(x3);

下面是求解结果：
Global optimal solution found.
Objective value: 0.4000000E-09
Objective bound: 0.000000
Infeasibilities: 0.1078671E-05
Extended solver steps: 29
Total solver iterations: 2154

Variable Value Reduced Cost
M 0.000000 1.000000
X1 1.620818 0.000000
X2 1.520772 0.000000
X3 1.570799 0.000000

Row Slack or Surplus Dual Price
1 0.000000 -1.000000
2 -0.3986220E-08 0.000000
3 -0.3970912E-06 0.000000
4 -0.1078671E-05 0.000000

Answer 2

min=m;
@cos(x1)+@cos(x2)+@cos(x3)=3.14/4*3*m;
@cos(5*x1)+@cos(5*x2)+@cos(5*x3)=0;
@cos(7*x1)+@cos(7*x2)+@cos(7*x3)=0;
@free(x1);
@free(x2);
@free(x3);

下面是求解结果：
Global optimal solution found.
Objective value: 0.4000000E-09
Objective bound: 0.000000
Infeasibilities: 0.1078671E-05
Extended solver steps: 29
Total solver iterations: 2154

Variable Value Reduced Cost
M 0.000000 1.000000
X1 1.620818 0.000000
X2 1.520772 0.000000
X3 1.570799 0.000000

Row Slack or Surplus Dual Price
1 0.000000 -1.000000
2 -0.3986220E-08 0.000000
3 -0.3970912E-06 0.000000
4 -0.1078671E-05 0.000000