- .
- - .
.
:
(3.1)
(3.2)
(3.3)
(3.4)
.
1. - (.1).
, F : pj, qj.
.1
-x1 -x2 -x m | 1 | |
y1= y2= - ym= | a 11 a 12 a 1n a 21 a 22 a 2n a m1 a m2 a mn | a 1 a 2 a m |
F1= F2= | -p1 -p2 -p m -q1 -q2 -q m | 0 0 |
2. . 1 , F2 = 0, b 䒺 .
, .
k (.2).
.2
-y 1 -y 2 -y k -x s -x n | 1 | |
1= 2= k= Yr= Ym= | b 11 b 12 b 1k b 1s b 1n b 21 b 22 b 2k b 2s b 2n b k1 b k2 b kk b ks b kn b r1 b r2 b rk b rs b rn b m1 b m2 b mk b ms b mn | b 1 b 2 b k b r b m |
F1= F2= | - p1 -p2 -pk -ps -pn -q1 -q2 -qk -qs -qn |
bj 䒺. F1 F2 P(k) Q(k), Q(k) ¹ 0, .
³ , Fmax , (.7).
.7.
brs. , brs ( ). brs. (k+1) - P(k) :
(3.4)
i Q(k) :
(3.5)
(k+1)- :
.
:
(3.6)
:
(3.7)
:
(3.8)
(3.8)
1. ,
, , . , .
2. Q(i) > 0, Q(k)×Q(k+1) > 0, F(k+1) F(k) ds. ds > 0, F(k+1) F(k) < 0. F(k+1) < F(k) F(k) > F(k+1).
,
ds > 0, , ds < 0, F(k) > F(k+1) .
ds = 0, F(k+1)=F(k) .
ds brs.
.
1. ϳ :
|
|
,
.
, F1 i F2
(.3):
.3
-y 1 -y 2 -x s -x n | 1 | |
1= 2= ym= | b 11 b 12 b 1s b 1n b 21 b 22 b 2s b 2n b m1 b m2 b ms b mn | b 1 b 2 b m |
F1= F2= | p 1 p 2 p s p n q 1 q 2 q s q rn | 0 0 |
dj= | d 1 d 2 d s d n |
2. , dj < 0. , , dj .
3. .
4. brs F1 F2 , .
5. dj, - F(k+1). dj 䒺, . .
6. , dj 䒺.
7. , dj > 0. dj.
.
:
:
.
, F1 F2 (.4).
.4
1 | -x 1 - 2 -x 3 | |
y1= y2= y3= | -3 6 1 -1 7 2 -2 4 -1 | -1 |
F1= F2= | 1 2 -1 3 1 5 |
b3 = -1 < 0, 1 = 2 = 3 = 0 .
. ³ , , dj F (.5).
.5
2 | -x 1 - 2 -y 3 | |
y1= y2= x3= | -5 10 1 -5 15 2 2 -4 -1 | |
F1= F2= | -3 2 1 7 -21 -5 | -1 |
dj | -8 -11 0 | -1/5 |
dj , ,
x1 = 0, x2 = 0, x3 = 1
. brs = 10. , , dj. (.6).
.6
3 | -x 2 -y 1 -y 3 | |
x2= y2= x3= | -1/2 1/10 1/10 5/2 -3/2 ½ 0 2/5 -3/5 | 1/10 17/2 7/5 |
F1= F2= | -2 -1/5 4/5 -7/2 21/10 -29/10 | 28/5 7/5 |
dj= | -92/5 11/10 11/5 | -12/71 |
䒺 , .
(.7).
.7
4 | -y 2 -y 1 -y 3 | |
x1= x2= x3= | 1/5 -1/5 1/5 2/5 -3/5 1/5 0 2/5 -3/5 | 9/5 17/5 7/5 |
F1= F2= | 4/5 -7/5 6/5 7/5 0 -11/5 | 28/5 19 |
dj= | 184/25 -133/5 878/25 | 28/15 |
䒺, . (.8).
|
|
.8
5 | -y 2 -y 1 -x 3 | |
x1= x2= y3= | 1/5 1/2 -1/10 2/5 3/2 -7/10 0 5/2 -3/2 | 5/2 11/2 7/2 |
F1= F2= | 4/5 -7/2 -9/10 7/5 0 -11/5 | 21/2 |
dj= |
.8 dj 䒺. , . .