lingo编程练习题.doc
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lingo编程练习题.doc
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一、编写lingo程序求解下列方程(组)
1、
symsx;
>>x=solve(x==(cos(x)+sin(x))/4)
x=
0.31518244283873590195648706093983
2、
>>symsx;
>>x=solve(x==4-2^x)
x=
4-lambertw(0,16*log
(2))/log
(2)
>>x=eval(x)
x=
1.386166980071494
3、求方程在中的根的近似值.
Matlab:
symsx;
>>y=x^3-2*x^2-4*x-7;
>>x=eval(solve(y))
x=
3.6320+0.0000i
-0.8160-1.1232i
-0.8160+1.1232i
OR:
symsx;
>>a=[1,-2,-4,-7];
>>x=roots(a)
x=
3.6320+0.0000i
-0.8160+1.1232i
-0.8160-1.1232i
Lingo:
x^3-2*x^2-4*x-7=0;
@bnd(3,x,4);
Feasiblesolutionfound.
Infeasibilities:
0.5329071E-14
Extendedsolversteps:
5
Totalsolveriterations:
36
VariableValue
X3.631981
Matlab:
functiony=f(m,n)
symsxxk;
a=m;b=n;
ff=x^3-2*x^2-4*x-7;
whileb-a>0.00001
xk=(a+b)/2;
fx=subs(ff,x,xk);
fa=subs(ff,x,a);
iffx==0
y=xk;
break;
elseiffa*fx<0
b=xk;
else
a=xk;
end
y=xk;
end
y=3.631980895996094
4、
symsx4;
>>x4=solve(x4^2-3*x4-4==0,x4)
x4=
4
-1
lingo
x1^2-3*x1-4=0;
x2^2-3*x2-4=0;
@free(x2);
VariableValue
X14.000000
X2-1.000000
5、
symsx1x2x3x4;
>>[x1,x2,x3,x4]=solve(2*x1+x2-x3+x4,3*x1-2*x2+x3-x4,x1+4*x2-3*x3+5*x4,x1,x2,x3,x4)
x1=z/7
x2=(5*z)/7
x3=z
x4=0
6、
a=[5,2,1;-1,4,2;2,-3,10];
>>b=[-12;20;3];
>>x=inv(a)*b
x=
-4.000000000000000
3.000000000000000
2.000000000000000
二、编写lingo程序求解下列最优化问题
1、
4*x1-x2+2*x3-x4=-2;
x1+x2-x3+2*x4<14;
-2*x1+3*x2+x3-x4>2;
@free(x4);
Feasiblesolutionfound.
Infeasibilities:
0.000000
Totalsolveriterations:
2
VariableValue
X10.000000
X21.000000
X30.000000
X41.000000
2、
3、
max=3*x1-x2;
3*x1-x2<3;
5*x1+4*x2>10;
2*x1+x2<5;
@gin(x1);
@gin(x2);
Globaloptimalsolutionfound.
Objectivevalue:
1.000000
Objectivebound:
1.000000
Infeasibilities:
0.000000
Extendedsolversteps:
0
Totalsolveriterations:
0
VariableValueReducedCost
X11.000000-3.000000
X22.0000001.000000
4、
5、
min=3*x+7*x2-x3+x4;
2*x1-x2+x3-x4>1;
x1-x2+6*x3+4*x4>8;
5*x1+3*x3+x4>5;
@bin(x1);
@bin(x2);
@bin(x3);
@bin(x4);
Globaloptimalsolutionfound.
Objectivevalue:
0.000000
Objectivebound:
0.000000
Infeasibilities:
0.000000
Extendedsolversteps:
0
Totalsolveriterations:
0
VariableValueReducedCost
X0.0000003.000000
X20.0000007.000000
X31.000000-1.000000
X41.0000001.000000
X11.0000000.000000
6、求图中点到各点的最短路(不可逆行).
7
4
v2
v4
v3
v1
v5
v6
v7
2
5
3
2
4
6
3
3
4
2
1
v8
model:
SETS:
points/v1,v2,v3,v4,v5,v6,v7,v8/:
L;
roads(points,points)/
v1,v2v1,v3v1,v4
v2,v3v2,v5v3,v6v4,v3
v6,v5v6,v8v7,v6v7,v4v8,v5v8,v7/:
d;
ENDSETS
DATA:
d=253
2464
342731;
L=0,,,,,,,;
ENDDATA
@FOR(points(i)|i#GT#@index(v1):
L(i)=@MIN(roads(j,i):
L(j)+d(j,i)););
end
Linearizationcomponentsadded:
Constraints:
24
Variables:
14
Integers:
10
Feasiblesolutionfound.
Infeasibilities:
0.000000
Extendedsolversteps:
0
Totalsolveriterations:
0
VariableValue
L(V1)0.000000
L(V2)2.000000
L(V3)4.000000
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