ДО Карагодова

b

(b1, ..., bm ) , A

aij

,

c

(c1 , ,cn )

% -

i 1, n

[19].

j 1,m

E( ! =

:

’

D @ <

%

-

' G , %

G .

%

!

D @ <

' , % '

!-

! :

-

1.

" ! ’

’ .

-

2.

! - ' ,

! ’ , < =:

D @ T j % ’% , %

.

3. "’ , % !

T j 0 ,

xkj

0

(k 1,2, ,m) .

D @ %, ’ %, <-

! ' ' . D @ -

xkj

T j 0 % ( !

!- T j

0 % !

xkj 0 ), % .

4. : ! j

0

( ! Ts ), !

s

xko

k ,

x

ks

0

-

x

ks

.

A min

xko

l .

xks 0

xks

5. " ’ , ! -

' = = xl

= xs .

-!

&

<

.

" ,

%

T j

0 , %

( s ).

" ,

! ’ , %

( l ).

-

-! ,

, %

-

( xls ).

* =

k -

p(k) [aio(k) , ai(1k) , , ain(k) ],

i

A

1,m

<

!

p(k 1)

—

A

(k 1) - :

l

a(k 1)

ali(k )

,

i 0,

1,

...,

n ,

(2.4)

als(k )

li

a(jsk 1) 0; j

1,m

, j s, als(k 1) 1,

(2.5)

a

(k )

a(k 1)

a(k )

lj

a(k) ,

j s,

(2.6)

als(k )

ij

ij

is

i l.

n

aij xi bj

, j 1,m .

(2.7)

i 1

A !

xi 0,

i

,

(2.8)

1,n

% <

n

f (

x

) ci xi .

(2.9)

i 1

n

( 2.7 )

aij xi

y j

bj , j 1,m,

i 1

xi 0, i

,

y j 0,

j

,

( 2.8 )

1,n

1,m

n

m

max .

( 2.9 )

F(

x

,

y

) ci xi

M y j

i 1

j 1

= < , ,

@

( 2.7 )—( 2.9 ) % ’ , y j

==

<

Zi (

x

)

f (

x

)

extr,

(2.10)

u(x)

f (

n

m

x

) ci xi , U(

x

) di xi 0

i 1

i 1

x

, @

' !

& ’ =

!- .

" "&E( - < :

"

x

0,

(2.11)

@ ' ! G , :

(2.12)

Ax

b

= <

f

x

Z

U

max (min) .

(2.13)

x

&

’

!-

,

Z max

).

(

& '

(2.11)—(2.13),

Z max . A ! = =

’

% -

' ' , !

& .

(2.14)

=

x

X , !

U

n

d j xj 0

X .

(2.15)

x

x

j 1

' & < U

= ,

x

, @ < U

' &:

x

U

0

X .

(2.16)

x

x

A

! ' , @

"&E( % -

(2.16).

/(

% ' -

!

-

<

U

'

x

yi

xi

1

(2.17)

, i 1,n ,

yn 1

n

n

di xi

di xi

i 1

i 1

yi 0, i

1, n 1

,

(2.18)

@ ' ! G1 , ! ' :

n

aij yi bj yn 1

0 , j 1,m ,

(2.19)

i 1

n

(2.20)

di yi

1

i 1

= < =

n

max .

(2.21)

Z ci yi

i 1

' .

0 "&E( -

1. ) '

x

0

& ,

0 — "&E(. !

x

0

n

0

0

, @ %

U x

di xi

. " (2.16) U x

0

i 1

0 y10 ,..., yn0 , yn0 1 : yi0

xi0

,

i

; yn0 1

1

y

1,n

0

0

U x

U x

, @

0 ’% .

y

0

(2.19), (2.20) '

: y % ! '

0

0

n

aij xi

bj

U x . ' :

i 1

n

a0i yi0

bj

yn0 1 . B ' %

j 1,m , ! !-

i 1

0

0

'

(2.19) y

' = . ( ' , @ y -

% (2.20):

n

0

0

n

n

0

U x

di xi

di yi0 di

xi

i 1

1 ,

i 1

i 1

0

0

U x

0

U x

U x

yn0 1 0

' "E( % -

0 "&E(,

! ==

x

0

y

< :

y0

x0

i

, i 1,n .

(2.22)

i

yn0 1

A ’%

0 . ( ' , @

x

0 % ’ "&E( (2.11)—(2.13).

x

n

bj yn0 1 , yn0 1 0 /

" aij yi0

i 1

' , @ < U

!-

x

' ' $/, :

1

n

0

n

yi0

n

0

,

b

a

y

a

a

x

j

ij

i

ij yn0 1

ij

i

yn0 1 i 1

i 1

i 1

@

j

. ' ,

0 X .

1,m

x

n

0

n

0

yi

ci

ci yi0

yn 1

0

0

n

f

ci yi0

i 1

i 1

yn 1

x

.

n

n

0

0

i 1

d

y0

yi

U x

0

di

i 1

i

i

yn 1

0

i 1 yn 1

A ' % ' .

4. D @

% ’ '

y

! ==

"E(, x , (

= = :

" xi 0, i

1,n

,

(2.23)

! G , :

n

gij (xi ) bj , j

1,m ,

(2.24)

i 1

= < =:

n

F(

x

) fi (xi ) .

(2.25)

i 1

n

f (

x

) fi (xi ) .

(2.26)

i 1

!-= < %=

fˆ(

x

)

[19], [25].

)

: = = ' , f j (xj )

( j

1,n

!-

ˆ

) ; gij (x j )

ˆ

(x j ) .

f j (x j

— gij

# (2.23)—(2.25) % ! ' :

" xj

0,

j

1,n

,

( 2.23 )

!

ˆ

G , ! ' :

n

,

ˆ

)

bi

,

i

1,m

gij (x j

( 2.24 )

j 1

= < =:

ˆ

n

ˆ

(xj ) .

( 2.25 )

F(x) fj

j 1

: ’

!

' :

< gij (x j )

f j (x j ) ;

1. & !-

2. ( ! = .

’ -

3. "

-

@

gij (x j ) f j (x j ) = , ! = -

% , ! '