Введение в специальность / 13 - Vv_v_sp_11 - zad pr
.pdf!" |
|
# $ %&'( )* +, - . / 0/ 1/2 3 / 45 |
|
1/ / 6 1 7 8 9 / 7 6 1 7 / 6 74 2 4 403 |
|
1/ 6 7/ 6 : 7 40 6 1 7 ; </7/= |
|
/ 6 / > 0 7 8 1 / 7 6 1 7 1/ ? / /= |
|
8 @ 7 :A / 64 / 6 74 2 4?5 8 1/ / 6 1= |
|
7 8 9 / 3 6 7 8 8 0 6 1 7 /3 |
|
: 6 /? 6 1 7 ? / / > 4? 6 : > ; |
|
:5 6 1 7 / 6 7 !# $ B%#&CC D * ECFG |
&D |
)H I - 6 /? 94 2 ? 3 /@/?54? 4? 1/ > |
#J " |
EBF, 6 74 2 !,% ,% ; K :8 7 > 14 H I / / |
= |
4 3 / / / 4 1 / / 6 : / / 1/ 9 9 = |
|
6 >14 8 4 / 14 > / 6 1 7 = |
|
7 > ; L/ 6 / 3 6 76 /0/ 3 9 / 64 / |
|
7 7 6 74 2 6 >14 7 6 1 7 / m !# $ B%#&C"
C JM |
* ,F%# ; N: 1 / 1 |
xi |
1/ / i=0 |
9 / /3 |
i I |
= {1, . . . , m}; B% ,CB%# |
* ,F%# X |
/ @ 7 = |
|
2/ > / m= 0 7 / 6 / / O |
||||
|
X = R+m = {x Rm: xi ≥ 0, i I} , |
|
||
3 :5 0 3 07/ 6 / 7/ 1=1/ 0 / |
4 ; |
|||
H 4 : / > @ |
|
|
||
X = {x Rm+ : g(x) ≤ 0} ,
07 g(x) = (g1(x), . . . , gk(x)) . k= / 94 2 0 / / 9 / ; I/ 1 ? : / 4 / > 8 3 : 7 @ 8 7 2/8 ;
P/ / !# $ B%#&CC D * ECFG &D /1 /? 2/= > 4? 94 2 ? Q = f (x) 3 / 54? /@ 7 x 6 / / 9 / =
X :A 64 / Q 47 ?54? / ;
1 6 1 7 8 94 2 6 > QRST 0;3 07/ 6 / > / > / / 8 4 8 U ;L ::/ H ;U 40 / / VW 6 1 7 /X )7 1/7/ - 6 6 1 7 4? 94 2 ? 7/
Q = AKαLβ , )T ;Q-
07 K . /6 / 3 L . 47 4 3 Q . :A 645 6 74 = 2 3 A3 α3 β . 6/ / )A > 0 3 α, β ≥ 0 3 α + β = 1-; Y 8
Z[
6 |
94 2 ? 7 / )T ;Q- /1 /? H I L::/ U 40/ /; ? 7 40 |
6 H I ; |
|
|
H 6 17 4? 94 2? 7 74?5 6 17= |
1/7/ ; K 676 10 7 7 4? 6 74 2? 3 |
|
6>14 6 n 8 08 6 2 ; U 10 6= |
|||
742 :4? 1// 61 7 8 9 / 3 7 8 |
|||
04 /// > / > // 3 / /6 / 3 47 3 1 = |
|||
. & # C J & |
!# $ B%#&CC J & * ,F% J ; 74 , " |
||
& |
#,CC, +$ &'( |
6 1 7 /3 3 / 6 / 3 / 6 = |
|
1 7 8 9 / / / /? > 47 /6 / 3 6 7 |
|||
> 4 / 4? 4 4 /6 / /; N7 / / 4 |
|||
7 > 0 6 76 9 ) ; ; / 4-3 07 :4 |
|||
:> |
|
/ 7 / 1/2 7 3 7 489 / 6 1 7 94 2 |
|
|
|
|
|
04 : > > / 0 4: ; |
|||
H4 > 6 1 7 8 9 / / m; N: 1 / = |
|||
1 xi 3 i I = {1, . . . , m}3 ) 4?5 8 7 2/8 1 =- i=0 9 / /3 ?5 0 4 6 76 3 aij . i=0 9 / /3 1/ / / 0 j= 8 0 6 2 6 70 94 2 / 3 j J = {1, . . . , n}; =
> j=0 8 0 0 6 2 / / / zj 3 |
P aij zj . i=0 |
||||||
|
|
|
|
|
|
j J |
|
6 1 7 0 9 / /3 745 0 / 6 1 7 6 74 2 3 6 |
|||||||
6 ? / / |
|
|
|
|
|||
|
X aij zj ≤ xi, i I. |
|
)T ;S- |
||||
|
j J |
|
|
|
|
|
|
aij , |
j J |
|
|
|
|
||
P/ 24 A = |
i I |
|
/1 /? + ,% |
G&D !,% ,% ; H = |
|||
3 ? 0 / / 3 6 4 |
|||||||
/ @ > / 8 0 / |
|
|
|||||
|
d |
j |
≤ z ≤ d , j J. |
|
)T ; - |
||
|
|
|
j |
j |
|
|
|
N: 1 / 1 z(x) = (zj (x), j J ) #&F% |
C%&CB #C B%&D 0 |
||||||
6 1 7 / /1 0 ',C + 3 47 0 / |
|||||||
)T ;S-3 )T ; - 6 1/7/ x = (xi, i I) ; P @ 8 6 /
: 1 / 1 Z(x) ; U / 3 : 1 / 1 qj !# $ %&'(C B%( j"%&MC ' &BF G&BB, 3 ; ; 64 / 6 74 2
) 4?5 8 7 2/8 1 - 6 5 >? j=0 8 0 = 0 6 2 / 6 7 0 94 2 / ; W/
: /1 3 6 6 / z(x) :5 :A 64 / 6 76 6 74 = ZZ
2 /
Q(z | x) = X qj zj (x). |
)T ; - |
j J |
|
K/ 2 3 6 > 4 ? : 1 9 / |
0/ |
3 /@ > 0/ |
|
b i ≤ xi ≤ bi , i I. |
)T ; - |
/ 9 4 2? |
|
f (x) = max Q(z | x), b ≤ x ≤ b , |
)T ; - |
z Z(x) |
|
b = (b i, i I) 3 b = (bi , i I) ; N / /@/ 1/ > @74 64 = |
|
6742 1// / ) / 9 4 2 3 / /1/ 3 /1 /? |
|
6 1 7 -; H // 0 :5 9 4 2? )T ; - /1 |
|
!# $ B%#&CC D * ECFG &D !,$ , |
,C,' !, B B # !# $ " |
B%#&CC D $ & %&'(C B% ; |
|
H /@ 7 x 1 / 94 2 )T ; - @ / / 0 ; |
|
/ 7 3 6 7 : 1/6 3 0 / )T ;S- )T ; -3 1 / f (x) 6 1/7/ x / f (x) = Q(z0(x) | x) 3 07 z0(x) . 1/7/ H O
q 0z → max, Az ≤ x, d ≤ z ≤ d , )T ; -
q = (qj , j J ) . 6 1 7 > 3 d = (d j , j J )3 d =
dj , j J |
|
; W/ : /1 3 7 / 6 6 1 7 |
|
94 2 / / 6 7 H 1/7/ )T |
; -; |
N / 1/7/ / 7 0 0 6 / / 9 / = |
|
1/ ? / / 1/2 6 : / 6 / |
|
9 / O |
|
P (x) = p0f (x) − p 0x → max, x R+m, |
)T ;T- |
07 p0 . 2 / 6 1 7 9 6 74 2 3 x . #&F% !,% ,% 3 p =
(pi, i I) . #&F% |
G&C 9 / 6 1 7 /3 R = p0f (x) . $ M $ 3 |
|
C = p 0x . |
!$ & F |
!# $ B%#, ; |
</7/ / |
)T ;T- / : 6 3 4 /? 0 /= |
|
/ 1/ / 9 / 3 / / @ /? 1/7/ 2 / 6 74 2 ? 3 / 9 / ; 6 4 1/7/ )T ;T- 45 47 ?: 8 6 1 7 8 94 2 ; / 36 6 1 7 94 2 3 6 76 @ > 3
z ≥ 0 3 x ≥ 0 3 6 > 4 )T ;S-3 )T ; -3 )T ; - 1/7/ / )T ;T- 7 O
p0q 0z − p 0x → max, Az − x ≤ 0; z ≥ 0, x ≥ 0.
Z
K6 7 6 7 H 7 6 7 1/7/ |
|
6 /1 / 4 6 1 7 /; |
|
N7 / 3 / > 3 > /@ 7 0 6 2 / 0/ / |
|
? 79 2 9 / 3 1/7 // |
9 |
; 4 / 1/7// )T ;T- 6 / 7 O |
|
p0q 0z − p 0x → max, Az − x ≤ 0; d ≤ z ≤ d , b ≤ x ≤ b .
1/7// H @ : > 7 // 6 5 >? 7 H ;
Z