min Z =
j ≤ xj ≤ bj; j = 1 ÷ n,
.
1. ω(j ≤ xj ≤ bj); j=1÷n.
2. (1, 2,..., n) = (x1 , x2 ,,xn ) = (x10, x20,..., xn0), ω.
3. Z = .
4. = , Z = f().
5. S = 0, N = 1000 .
6. λ.
7. , Î w, xj1 = xj +λj ּxj = j + λj ּbj.
8. = , Z = f().
9. f() f().
10. , f() <f(), 11, 12.
11. = Z =f() = f().
12. 7.
13. f() ≥ f(), S = S + 1.
14. S N, N . S ≤ N, 7, 15.
15. . Z =f() .
18
minZ = (x1 - 2)2+(x2 - 1)2
0 ≤ x1 ≤ 3,
0 ≤ x2 ≤ 2.
I .
1. ω:
ω 0 ≤ x1 ≤ 3,
0 ≤ x2 ≤ 2.
2. (x1 , x2 ), (0,0).
3. Z= (x1 - 2)2+(x2 - 1)2
4. = , Z =f() = + = 5
S = 0.
5.
λ (0,11; 0,17; 0,20; 0,09; 0,15; 0,71; )
6.
= xj + λj ּ xj
= 0 +0,11*3 = 0,33
= 0 +0,17*2 = 0,34
= (0,33; 0,34) Î ω
7. = ; Z = f(); Z = f() = (x1 - 2)2+(x2 - 1)2= + = (1,67)2 + (0,66)2 = 2,79 + 0,44 = 3,23
8. f() f(), 3,23 < 5, .
9. = (0,33; 0,34); Z =f() =f() = 3,23
II
1.
= 0 + 0,20*3 = 0,60
= 0 + 0,09*2 = 0,18
(0,60; 0,18) Î ω
2. Z =f() = + = (1,40)2 + (0,82)2 = 1,96 + 0,67 = 2,63
3. f() f()
2,63 < 3,23, .
4. = (0,60; 0,18)
Z=f() = f() = 2,63
. .
8
1-15 , , .
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
|
|
. : = xj0 +Pj , - , ,
=1, . . = + 1.
, - , ≤ Pj ≤ . , [-1, 1]. Pj =A+ λjּB, λj - λ.
, = xj0 + (A+ λjּB) .
= - e.
9
1-15 8 , , ..
, .. . .
1. w, .. .
w. . , =100. S=0 .
2.
.
3.
4. , Î w, ,
li .
5. .
6. ≤ , 7, 8.
7. ( = ) = .
4.
8. > , , S = S + 1.
9. S ≤ N, N , , N=1000, . 10.
10. . .
. (̮¥) 0, .. . ,
. .
19
1. w:
0 ≤ 1 ≤ 4 10 = 1 = 0;
0 ≤ 2 ≤ 4 20 = 2 = 0;
= 10
: (0,44; 0,19; 0,36; 0,91; 0,25; 0,31; 0,11; 0,14; 0,17; 0,24; 0,16; 0,47; ).
S = 0 .
2. :
3. (0;0).
4. :
= 1 + lj·1
= 0+0,44 · 4 = 1,76
= 2 + l2·2
= 0+ 0,19· 4 = 0,76
(1,76; 0,76) Îw
5. :
|
|
w Z() = (1,76 1)2 + (0,76 1)2 + 10 · (1,76 + 0,76 4)2 = (0,76)2 +
+ (-0,24)2 + 10 · (1,48)2 =0,5776 + 0,0576 +20,904 = 21,5392
6. w Z() :
21,5392 < 162. .
7. , .. (1,76; 0,76).
= = 21,5392.
8. :
= 0+ 0,36 · 4 = 1,44
= 0 + 0,91 · 4 = 3,64
(1,44; 3,64) Ï w, .. 1,44 + 3,64 = 5,08, 1 + 2 ≤ 4.
5,08 > 4.
9. :
= 0 + 0,25· 4 =1
= 0 + 0,31 · 4 = 1,24
(1; 1,24) Î w
10. :
w Z() = (1 1)2 + (1,24 1)2 + 10 · (1 + 1,24 4)2 = 02 +
+ (0,24)2 + 10 · (1,76)2 =0 + 0,0576 +30,946 = 31,0036.
11. w Z() :
31,0036 > 21,5392. .
12. : S = S + 1; S = 0 + 1; S = 1.
13. S < 3, 3 .
14. :
= 0 + 0,11 · 4 =0,44
= 0 + 0,14 · 4 = 0,56
(0,44; 0,56) Î w
15. :
w Z() = (0,44 1)2 + (0,56 1)2 + 10 · (0,44 + 0,56 4)2 =(0,56)2 +
+ (0,44)2 + 10 · (3)2 =0,3136 + 0,1936 +90 = 90,5072.
16. w Z() :
90,5072 > 21,5392. .
17. : S = S + 1; S = 1 + 1; S = 2.
18. S < 3, 3 .
19. :
= 0 + 0,17 · 4 =0,68
= 0 + 0,24 · 4 = 0,96
(0,68; 0,96) Î w
20. :
w Z() = (0,68 1)2 + (0,96 1)2 + 10 · (0,68 + 0,96 4)2 =(0,32)2 +
+ (0,04)2 + 10 · (2,36)2 =0,1024 + 0,0016 +55,696 = 55,8.
21. w Z() :
55,8 > 21,5392. .
22. : S = S + 1; S = 2 + 1; S = 3.
23. S = 3, 3 . , :
X* = (1,76; 0,76); min Z =21,5392.
20
min Z=9x12+9x22+12x1-6x2
0≤x≤4
1≤ x2≤5
.
:
Z=9x12+12x1+9x22-6x2 = 9(x12+ x1) + 9(x22- x2);
Z = 9(x12+2 x1+())+9(x22- x2)= 9(x12+2 x1+())+9(x22- x2) - - 9 - ;
Z = 9(x1+ )2+9(x2- )2-4-1==9(x1+ )2+9(x2- )2-5
C11=C22=9 ─ O1(; ).
Min Z=3 *(0;1).
0:
x10 =X1 =0;
x20 =X2 =1.
0(0;1) .
2. M = 0,01, N=3 .
(0,44;0,19;0,36;0,91;0,25;0,31;0,11;0,14;0,17;0,24;0,16;0,47)
S= 0 -
3. Z ( 0)= Z(0,1)=12-6=3
4.
WZ(x) = f(x)+(φ1( ))2+M(φ2( ))2++ M(φm(X))2
5. (0;0).
WZ( 0) = 9x12+9x22+12x1- 6x2+0,01(x1-4)2+0,01(x2-5)2 +0,01(1-x2)2
WZ( 0) = 3+0,0116+0,0116 +0,010 = 3,32.
6. :
= 1 + lj·1
= 0+0,44 · 4 = 1,76
= 2 + l2·2
= 1+ 0,19· 5 = 1,95
(1,76; 1,95) Îw
5. :
wZ() = 9(1,76)2 + 9(1,95)2 + 12·1,76-6·1,95+0,01 · (1,76 4)2 +0,01 · (1,95 5)2 +0,01 · (1-1,95)2 = 71,66224.
11. wZ() :
71,66224 > 3,32. .
12. : S = S + 1; S = 0 + 1; S = 1.
13. S < 3, 3 .
14. :
= 0 + 0,36 · 4 =1,44
= 1 + 0,91 · 5 = 5,55
(1,44; 5,55) Ï w .
|
|
12. : S = S + 1; S = 1 + 1; S = 2.
13. S < 3, 3 .
14. :
= 0 + 0,25 · 4 =1,0
= 1 + 0,31 · 5 = 2,55
(1,0;2,55) Îw
15. :
wZ() = 9· 12 + 9(2,55)2 + 12·1,0 - 6·2,55+0,01 · (1,0 4)2 +0,01 · (2,55 5)2 +0,01 · (1 - 2,55)2 = 64,39655.
11. wZ() :
64,39655 > 3,32. .
12. : S = S + 1; S = 2 + 1; S = 3.
13. S = 3, 3 . .
* = 0(0;1), WZ( 0) =3,32;
min Z = Z ( *)= Z(0,1)=12-6=3
. , , 1000.
10
1-15 8 , , .
()
, , - .
X1 X2.
Z(X1,X2)= C11X12+C12X1X2+C22X22+C1X1+C2X2 +C0
aI1 X1 +aI2X2.≤ aI 0 , i=1÷n, X1≥0, X2≥0
, ( ). - : , , , . , C12=0, .
1 . ) C11=C22>0.
Z(X1,X2)= C11X12 +C22X22+C1X1+C2X2 +C0 Z(X1,X2)= C11(X1 -a)2 +C22 (X2-b)2+C0 . O`(a,b).
) C11=C22<0.
Z(X1,X2)= C11X12 +C22X22+C1X1+C2X2 +C0 Z(X1,X2)= C11(X1-a)2 +C22 (X2-b)2+C0 . O`(a,b).