qi = Di (p)
p=
⇥
q=
p
⇥
p
q
i 8i = , , ..., n
⇤
· · · pn
⇤
q · · · qn
c(q , q , ..., qn )
qi = Di (pi )
c(q , q , ..., qn ) = c(q ) + c(q ) + ... + c(qn )
n
i
Li =
piM ci
=
✏i
piM
máx
p ,p ,...,pn
⇧=
(
n
X
pi Di (p)
c(D (p), D (p), ..., Dn (p))
i=
n=
[p ] :
[p ] :
@⇧
=
@p
@⇧
=
@p
[p ] :
@⇧
=
@p
)
p
p
@D (p)
@D (p)
@D (p)
+ D (p) + p
+p
@p
@p
@p
@c(•) @D (p)
@q
@p
[pi ] : pi
@c(•) @D (p)
=
@q
@p
X @Dj (p)
@Di (p)
+ Di (p) +
pj
@pi
@pj
j6=i
8i 8j 6= i 8k
@c(•) @D (p)
@q
@p
n
X
@c @Dk (p)
=
@qk @pk
k=
qi = Di (p)
c(q , q , ..., qn ) = c(q ) + c(q ) + ... + c(qn )
n=
máx ⇧ =
p ,p ,,p
p
[p ] :
X @Di (p)
i=
@p
(
X
pi Di (p)
i=
pi + D (p)
X
@c (•) @D (p)
@q
@p
| {z }
c 0 (•)
@c (•) @D (p)
=
@q
@p
| {z }
c 0 (•)
ci (Di (p))
i=
)
@c (•) @D (p)
@q
@p
| {z }
c 0 (•)
[p
c 0 ]D 0 (p) =
D (p)
[p
c0 ]
@D (p)
@p
c0 ]
[p
@D (p)
@p
/D 0 (p)p
c0 ]
[p
p
=
D 0 (p)
D (p) p
[p
c0 ]
@D (p)
@p D 0 (p)p
[p
c0 ]
@D (p)
@p D 0 (p)p
✏
c0 ]
[p
|
p
{z
L (p m )
}
=
|
D 0 (p)
D (p) p
{z
✏
}
z
}|
{
@D (p) p
p
D (p)
[p
c 0 ] @p D (p) p
D 0 (p)
p
| {z }
p D (p)
D (p)
L (p m )
| {z }
✏
✏
z
}|
{
@D (p) p
p
D (p)
[p
c 0 ] @p D (p) p
D 0 (p)
p
| {z }
p D (p)
D (p)
L (p m )
| {z }
✏
L (p m ) =
✏ (p m )
| {z }
L (p m )
↵i = pi Di (p)
L (p m )
L (p m )
+
✏ (p m )

L (p m )✏ (p m )
↵
↵
+ L (p m )✏
↵
↵
✏ij
✏
<
✏
<
L (p m ) < L (p m ) ) p < p m
✏
>
✏
>
L (p m ) > L (p m ) ) p > p m
t= ,
t=
q = D (p )
c(q )
t=
q = D (p , p )
c(q )
máx ⇧ = [p D (p )
p ,p
[p ] : p
@D (•)
+ D (•)
@p
[p
c 0 (•)]
c(q )] + [p D (p , p )
@c(•) @D (•)
+
@q
@p

⇥
@D (•)
+ D (p ) + p
@p
p
@D (•)
@q
c 0 (•)
c(q )]
@c(•) @D (•)
=
@q
@p
⇤ @D (•)
=
@p
[p
c 0 (•)]
=
p
[p
c 0 (•)] @D (•)
0
D (•)P
@p
D 0 (•)
D (•) p
t=
L (p m ) < L (p m ) =
✏
) p < pm
[p ] : p
[p
@D (•)
+ D (•)
@p
c 0 (•)]
=
p
D 0 (•)
D (•) p
=
@c(•) @D (•)
=
@q
@p
✏
) p = pm
) L (p m ) =
✏
q = D (p , p ) =
q = D (p , p ) =
p p
p p
p m p m q (p m , p m ) q (p m , p m )
⇧m
pm pm qm qm ⇧
PES m
PES m
⇧
qi = D(pi )
c(q , q , ..., qn ) = c (q , q , ..., qn ) + c (q , q ) + ... + cn (q , q , ..., qn )
máx
p ,p ,...,pn
⇧=
@D (p )
+ D (p )
@p
[p
pi Di (pi )
c(q , q , q , ..., qn )
i=
n=
[p ] : p
n
X
@c @D
@q @p
c 0 (•)]
=
p
D0
D
p
@c @D (p )
@q
@p
+
c 0 (•) c 0 (•)
+
p
p
@c @D (p )
=
@q
@p
L (p m ) =
@c
>
@q
✏ (p m )
@c
>
@q
L (p m ) > L (p m )
m
p >p
m
+
pm
[c 0 (•) + c 0 (•)]
@c
<
@q
@c
<
@q
L (p m ) < L (p m )
pm < pm
t=
q = D (p )
c (q )
t=
q = D (p )
c (q , q )
@c (•)
<
@q
máx ⇧ = p D (p )
p ,p
[p ] : p
c (D (p )) + [p D (p )
@c (•) @D
@q @p
@D
+ D (p )
@p
[p ] : p
@D
+ D (p )
@p
L (p m ) <
✏
c (D (p ), D (p )]
@c (•) @D
=
@q @p
@c (•) @D
=
@q @p
L (p m ) =
✏
q =
q =
p
p
c (q ) = k q
c (q , q ) = k q
pm pm qm qm
⇧m
"q
p m p m q m q m ⇧m
⇧
m