molp -...
TRANSCRIPT
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*
MOLP
MOLP
MOLP
*. Corresponding author, Email: [email protected]
های نوین در ریاضیپژوهش دانشگاه آزاد اسالمی، واحد علوم و تحقیقات
MOLP
yxy
x
1
t t
,
1 1
t
2 2 2
max
s.t.
max
s.t. ,
x y
y
c x d y
A x B y b
e y
A x B y b
1, nc x2, , nd e y1A
1 1m n1B1 2m n2A
2 1m n2B2 2m n
1
t t
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1 1
max
s.t.
x yc x d y
A x B y b
t
2 2 2
max
s.t.
ye y
A x B y b
( , )x y
y
x
11 1 . A x B y b
MOLP
MOLP
t
1
t
2
t
min
min
min
s.t.
,
p
c x
c x
c x
Ax b
x 0
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pc c cm nA
nxmb
{ | , } X xAx b x 0
MOLP
{ | } Y Cxx X
MOLP
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Cp n
it
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x XMOLP
x X
, Cx Cx Cx Cx
xy Cx
EX
NY
{ | ; , }E X x X x X Cx Cx Cx Cx
{ | }.N E Y Cx x X
x X
x X
Cx Cx
xy Cx
WEX
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WE { | ; } X x X x X Cx Cx
WN WE{ | }. Y Cx x X
E WEX X. N WNY Y
y Y
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s 0
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MOLP
Ny
MOLP
MOLP
t
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max
s.t.
c y
y Y
Ny Y
Ny Y
0s
M
t t
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s.t.
max
s.t.
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p
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s
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WN
max
s.t.
c y
y Y
WNy Y
WNy Y
M
tmax (s),
s.t.
max s
s
s.t. s1
s 0
p
Ms
c yy
y Y
y Y
s
tc y
MOLPi
N(y )i
ic eiei
i
N t
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t
,
y max y
s.t.
max
s.t.
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i i p
p
M
x y x s
x s
1 s
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Ax b
x 0
1 s
Cx y s
Ax b
x 0 s 0
y
KKT
N t
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t t
max y
s.t.
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x y x s1 s
Cx y
Ax b
x 0
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v C w A 0
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t t
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p
p
v 1
v C w A x
v 1 s
w b Ax
x 0 s 0 w 0
0K
t t t t, , ( ) 0 v C w A 0 x 0 v C w A x
t t t t, , ( ) 0p p v 1 s 0 v 1 s
t, , ( ) 0 w 0 Ax b w b Ax
t t , ( ),
{0,1}, 1,2, ,
n
j
K K
p j n
0 v C w A p 0 x 1 p
t t , ( ),
{0,1}, 1,2, ,
p p
i
K K
q i p
0 v 1 q 0 s 1 q
, ( ),
{0,1}, 1,2, ,i
K K m
t i m
0 w t 0 b Ax 1 t
s 0
Min -11 -11 -12 -9 - +9x 9xx x x x2 3 4 5 6 7
Min -11 -11 -9 -12 - +99xx x x x x1 3 4 5 76
Min -11 -11 -9 -9 - -12x x x x 12x x1 2 4 5 6 7
s.t. + + + + + =1x x x x x x x1 2 3 4 5 6 7
, , , , , , 0x x x x x x x1 2 3 4 5 6 7
N(0, 0, 0).y
yMax -M( + + )s s s1 2 31
s.t. = -11 -11 -12 -9 - +y 9x 9xx x x x2 3 4 5 6 71
= -11 -11 -9 -12 - +9y 9xx x x x x1 3 4 5 762
= -11 -11 -9 -9 - -12y x x x x 12x x1 2 4 5 6 73
+ + + + + + =1x x x x x x x1 2 3 4 5 6 7
, , , , , , 0x x x x x x x1 2 3 4 5 6 7
Max + +s s s1 2 3
s.t. = -11 -11 -12 -9y s x x x2 3 4 511
- +9x 9xx 6 7
= -11 -11 -9 -12 - +9y s 9xx x x x x1 3 4 5 72 62
= -11 -11 -9 -9 - -12y s x x x x 12x x1 2 4 5 6 733
+ + + + + + =1x x x x x x x1 2 3 4 5 6 7
, , , , , , 0x x x x x x x1 2 3 4 5 6 7
K
yMax 1
s.t. -11 11 12 9y 9x 9xx x x x2 3 4 5 6 71
-11 11 9 12 9y 9xx x x x x1 3 4 5 762
-11 11 9 9 12y x x x x 12x x1 2 4 5 6 73
1x x x x x x x1 2 3 4 5 6 7
, , , , , , 0x x x x x x x1 2 3 4 5 6 7
-11 11 12 9y 9x 9xx x x x2 3 4 5 6 7 11
-11 11 9 12 9y 9xx x x x x1 3 4 5 76 22
-11 11 9 9 12y x x x x 12x x1 2 4 5 6 7 33
1x x x x x x x1 2 3 4 5 6 7
0 11 12
s
s
s
v
1 3 1
0 11 111 3 2
0 11 111 2 3
0 12 9 91 2 3 4
0 9 12 91 2 3 5
0 9 9 121 2 3 6
0 9 9 121 2 3 7
1, 1, 11 2 3
0 (1 )x1 1
0 (1 )x2 2
0 (1 )x3 3
0 (1 )x4 4
0 x5
w K pv
w K pv v
w K pv v
w K pv v v
w K pv v v
w K pv v v
w K pv v v
v v v
K p
K p
K p
K p
(1 )5
0 (1 )x6 6
0 (1 )x7 7
, , , , , , {0,1}.2 3 4 5 6 71
K p
K p
K p
p p p p p p p
MOLP
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