.
, , , , , , -.
( ) :
(1.1) |
z = f (x1,x2,, xn)
1(x1,x2,, xn) 1,
(1.2) |
m(x1,x2,, xn) m,
f, 1, 2,.., m .
, . .
1) f, =0; j=1,2,, n;
2) , f ;
3) f ;
4) f ;
5) f.
, . , .
I. , , , . (a) (b) . (. 1)
p1 p2 |
p1 p2 |
p1
p2
0 . 1 x1
(2.1) |
P = (1 - λ)P1 + λ P2, 0 ≤ λ ≤ 1.
λ. 1 2. : , 1 2, .
II. f , :
f [(1 λ)P1 + λ P2] ≥ (1 - λ) f (P1) + λ f (P2).
Z= f (x1, x2) (. 2).
z
M1 M M2
0 x2
P1 P P2
x1
. 2
(2.2) |
M ≥ (1 - λ) M1 + λ M2.
, , 1, 2, 12. , .
|
|
III. f , :
f [(1 λ)P1 + λ P2] ≤ (1 - λ) f (P1) + λ f (P2).
. 2 Z= f (x1, x2). M1 = f (P1), M2 = f (P2),
(2.3) |
M ≤ (1 - λ) M1 + λ M2.
, , 12, 12. .
.
1. () () .
2. , (. 3)
3. , (. 3)
4. () , (. 4)
5. i (x1, x2,, xn); i=1,2,,m - (), ,
i (x1, x2,, xn) ≤ bi; xj ≥ 0; i=1,2,,m; j=1,2,,n,
().
y
y = f ( x)
y = f ( x)
0 . 3 x
y
y1 = f 1 ( x)
y2 = f 2 ( x)
0 x
. 4
. . . , . . . , .