lingo编程练习题Word格式.doc

lingo编程练习题Word格式.doc

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-0.8160-1.1232i

-0.8160+1.1232i

OR:

a=[1,-2,-4,-7];

x=roots（a）

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

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<

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

-4.000000000000000

3.000000000000000

2.000000000000000

二、编写lingo程序求解下列最优化问题

4*x1-x2+2*x3-x4=-2;

x1+x2-x3+2*x4<

14;

-2*x1+3*x2+x3-x4>

2;

@free（x4）;

0.000000

2

X10.000000

X21.000000

X30.000000

X41.000000

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:

0

0

VariableValueReducedCost

X11.000000-3.000000

X22.0000001.000000

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>

@bin（x1）;

@bin（x2）;

@bin（x3）;

@bin（x4）;

Globaloptimalsolutionfound.

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

6

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））;

）;

Linearizationcomponentsadded:

Constraints:

24

Variables:

14

Integers:

10

Feasiblesolutionfound.

L（V1）0.000000

L（V2）2.000000

L（V3）4.000000