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d
s
uc
h
a
s
:
P
o
l
a
k
a
nd
R
i
b
i
è
r
e
(P
R
)
[5],
F
l
e
t
c
h
e
r
(CD
)
[6]
.
O
b
s
e
r
v
e
t
h
a
t
i
n
t
h
e
s
e
a
l
go
r
i
t
h
m
s
t
h
e
s
c
a
l
a
r
k
c
a
n
b
e
c
a
l
c
ul
a
t
e
d
b
y
W
o
l
fe
[
7]
a
nd:
k
T
k
k
T
k
k
k
k
T
k
k
k
k
k
k
d
g
d
d
x
g
d
g
x
f
d
x
f
)
(
)
(
)
(
(4)
1
0
T
h
e
s
t
r
o
n
g
W
o
l
f
e
c
o
n
di
t
i
o
n
s
m
a
y
n
o
t
y
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l
d
a
di
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c
t
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o
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o
f
de
s
c
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n
t
u
n
l
e
s
s
2
1
.
I
n
e
qua
l
i
t
y
gi
ve
n
i
n
(4)
i
s
s
o
m
e
t
i
m
e
s
c
a
l
l
e
d
t
h
e
A
rm
i
j
o
c
o
n
di
t
i
o
n
.
H
a
ge
r
a
n
d
Z
ha
n
g
[
8]
w
e
r
e
p
r
o
po
s
e
d
a
CG
m
e
t
h
o
d
(H
Z
)
T
h
a
t
c
o
r
r
e
s
po
n
ds
t
o
t
h
e
f
o
l
l
ow
i
n
g
upg
ra
de
p
a
r
a
m
e
t
e
r
w
h
e
r
e
.
de
n
o
t
e
s
t
h
e
E
uc
l
i
de
a
n
n
o
rm
o
f
ve
c
t
o
r
s
:
,
,
m
a
x
k
HZ
k
HZ
k
w
h
e
r
e
(5
a)
,
,
m
i
n
1
1
k
k
k
g
d
(5b
)
,
2
1
1
2
1
1
1
k
T
k
T
k
k
k
k
k
T
k
HZ
k
g
y
d
y
d
y
y
d
(5c
)
h
e
r
e
,
0
i
s
a
c
o
n
s
t
a
n
t
.
In
t
hi
s
r
e
s
e
a
r
c
h
,
w
e
pr
o
pos
e
d
a
f
a
s
t
-
s
pe
c
t
ra
l
CG
a
pp
r
o
a
c
h
t
o
s
o
l
ve
un
c
o
n
s
t
ra
i
n
e
d
n
o
n
l
i
n
e
a
r
o
pt
i
m
i
z
a
t
i
o
n
i
s
s
ue
s
.
W
e
pl
a
n
t
o
i
n
v
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s
t
i
ga
t
e
t
h
e
s
t
a
b
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l
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t
y
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n
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g
l
o
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v
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n
c
e
pr
o
pe
rt
i
e
s
o
f
t
h
e
pr
o
po
s
e
d
a
l
go
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t
hm
a
n
d
pe
r
f
o
r
m
s
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pr
a
c
t
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c
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l
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put
a
t
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ra
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a
b
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fo
r
s
o
l
v
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g
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t
a
i
n
n
o
n
l
i
n
e
a
r
o
pt
i
m
i
z
a
t
i
o
n
p
r
o
b
l
e
m
s
w
i
t
h
t
h
e
w
e
l
l
-
kn
o
w
n
P
ow
e
l
l
r
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s
t
a
r
t
c
ri
t
e
r
i
o
n
[9]
.
T
h
e
r
e
m
a
i
nde
r
i
s
o
r
g
a
n
i
z
e
d
i
n
t
o
fo
ur
s
e
c
t
i
o
n
s
.
S
e
c
t
i
o
n
2
e
xpl
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i
n
s
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a
r
l
i
e
r
s
t
ud
i
e
s
of
s
p
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c
t
r
a
l
CG
m
e
t
h
o
ds
.
S
e
c
t
i
o
n
3
o
ut
l
i
n
e
s
o
ur
p
r
o
po
s
e
d
m
e
t
h
o
d.
S
e
c
t
i
o
n
4
c
o
n
t
a
i
n
s
t
e
s
t
s
,
r
e
s
ul
t
s
,
a
n
d
di
s
c
us
s
i
o
n
.
S
e
c
t
i
o
n
5
c
o
n
t
a
i
n
s
t
h
e
f
i
na
l
r
e
m
a
r
ks
.
2.
LI
TER
A
TU
R
E
R
EV
I
EW
O
N
S
P
EC
TR
A
L
C
O
N
JU
G
A
T
E
G
R
A
D
I
EN
T
M
ET
H
O
D
S
S
pe
c
t
r
a
l
CG
(S
CG
)
m
e
t
h
o
ds
a
r
e
a
c
o
m
m
o
n
CG
a
pp
r
o
a
c
h
f
o
r
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g(1).
It
w
a
s
o
r
i
gi
na
l
l
y
de
ve
l
o
pe
d
by
B
a
r
z
i
l
a
i
a
n
d
B
o
r
w
e
i
n
a
n
d
l
a
t
e
r
s
t
ud
i
e
d
by
s
e
ve
r
a
l
a
ut
h
o
r
s
[10
-
14
].
B
e
l
ow
i
s
t
h
e
ge
n
e
ra
l
S
CG
pr
o
c
e
s
s
s
y
s
t
e
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
do
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4
31
A
l
go
r
i
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m
(S
C
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S
te
p
1
:
C
h
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x
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d
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k
f
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W
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c
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5).
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te
p
3
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If
k
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,
t
h
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t
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p;
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w
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4
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If
2
1
2
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0
k
k
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k
g
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i
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e
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p
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p
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di
r
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c
t
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n
;
o
t
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e
d.
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p
5
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put
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p
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k
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t
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d
i
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r
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nt
s
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s
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t
hi
s
f
i
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l
d.
S
te
p
6
:
Co
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put
e
t
h
e
p
a
r
a
m
e
t
e
r
k
f
r
o
m
t
h
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s
t
a
n
d
a
r
d
CG
m
e
t
h
o
d
S
te
p
7
:
Ca
l
c
ul
a
t
e
t
h
e
n
e
w
s
e
a
r
c
h
p
a
t
h
1
k
k
k
k
k
d
g
d
.
S
te
p
8
:
S
e
t
t
h
e
i
t
e
ra
t
i
o
n
k
=
k
+
1
a
nd
go
t
o
S
te
p
2
.
D
uri
n
g
t
h
e
l
a
s
t
de
c
a
de
,
m
uc
h
e
f
fo
r
t
ha
s
b
e
e
n
de
v
o
t
e
d
t
o
de
ve
l
o
pi
n
g
n
e
w
S
CG
m
e
t
h
o
ds
.
O
n
e
o
f
t
h
e
o
l
d
s
t
udi
e
s
i
n
t
h
i
s
f
i
e
l
d
i
s
p
r
o
po
s
e
d
by
R
a
y
da
n
(R
)
[15
].
A
l
-
B
a
y
a
t
i
a
nd
A
b
dul
l
a
h
(B
A
)
[16]
i
n
t
r
o
duc
e
d
a
n
e
w
c
l
a
s
s
of
S
CG
m
e
t
h
o
ds
o
f
un
c
o
n
s
t
r
a
i
n
e
d
l
a
rge
-
s
c
a
l
e
o
pt
i
m
i
z
a
t
i
o
n
p
r
o
b
l
e
m
s
us
i
n
g
b
o
t
h
s
pe
c
t
r
a
l
a
nd
s
c
a
l
i
n
g
pr
o
pe
rt
i
e
s
f
o
r
t
h
e
i
r
s
e
a
r
c
h
pa
t
h
s
.
i
.
e
.
1
1
k
T
k
k
T
k
CD
k
d
g
g
g
0
0
01
.
0
,
1
1
1
1
1
1
k
T
k
k
T
k
k
T
k
BA
k
y
s
s
s
s
s
(6)
Al
-
B
a
y
a
t
i
a
nd
H
a
s
s
a
n
(B
H
)
[17]
i
n
v
e
s
t
i
ga
t
e
d
a
n
o
t
h
e
r
S
CG
m
e
t
h
o
d
t
o
s
o
l
ve
un
c
o
n
s
t
ra
i
n
e
d
o
pt
i
m
i
z
a
t
i
o
n
p
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b
l
e
m
s
.
1
1
k
T
k
k
T
k
CD
k
d
g
g
g
.
1
1
1
1
1
k
T
k
k
T
k
k
T
k
BH
k
d
g
d
y
d
g
(7)
L
i
u
a
n
d
J
i
a
n
g
(L
J
)
[18]
p
r
o
po
s
e
d
m
i
n
o
r
m
o
di
f
i
c
a
t
i
o
n
o
f
t
h
e
CD
m
e
t
h
o
d
s
o
t
h
a
t
t
h
e
s
e
a
r
c
h
di
r
e
c
t
i
o
n
s
pr
o
duc
e
d
a
r
e
a
l
w
a
y
s
dow
n
w
a
r
d.
A
m
i
xe
d
s
pe
c
t
r
a
l
m
e
t
h
o
d
(L
D
W
)
i
s
pr
o
pos
e
d
by
L
i
u,
e
t
a
l
.
[19
]
fo
r
s
o
l
v
i
n
g
s
o
m
e
n
o
nl
i
n
e
a
r
o
pt
i
m
i
z
a
t
i
o
n
p
r
o
b
l
e
m
s
.
,
,
0
,
0
),
,
0
(
m
i
n
1
e
l
s
e
d
g
if
k
T
k
CD
k
k
CD
k
L
D
W
k
1
1
1
1
k
T
k
k
T
k
L
D
W
k
d
g
d
g
(8)
)
)
(
1
(
1
1
1
k
k
k
k
T
k
L
D
W
k
g
g
d
d
g
(9)
L
i
v
i
e
r
i
s
a
n
d
P
i
n
t
e
l
a
s
(L
P
)
[20]
s
ug
ge
s
t
e
d
a
n
o
t
h
e
r
t
y
pe
of
S
CG
m
e
t
h
o
d
p
r
o
v
i
di
n
g
s
uf
f
i
c
i
e
n
t
de
s
c
e
n
t
di
r
e
c
t
i
o
n
s
,
r
e
ga
rdl
e
s
s
of
qua
l
i
t
y
l
i
n
e
s
e
a
r
c
h
a
n
d
g
l
o
b
a
l
c
o
n
v
e
r
ge
n
c
e
p
r
o
pe
r
t
y
fo
r
ge
n
e
ra
l
f
u
n
c
t
i
o
n
s
,
gi
v
e
n
t
h
e
l
i
n
e
s
e
a
r
c
h
t
e
c
hni
que
m
e
e
t
s
W
o
l
f
e
r
e
qui
r
e
m
e
n
t
s
.
A
n
o
t
h
e
r
n
o
v
e
l
S
CG
m
e
t
h
o
d
w
a
s
pr
o
po
s
e
d
by
A
l
-
Ba
y
a
t
i
a
nd
Al
-
K
h
a
y
a
t
(B
K
)
[21]
i
n
t
h
i
s
f
i
e
l
d
.
T
h
e
y
t
r
i
e
d
t
o
c
o
n
s
t
r
uc
t
a
d
e
s
c
e
n
t
di
r
e
c
t
i
o
n.
1
1
k
T
k
k
T
k
CD
k
g
d
g
g
,
1
1
2
1
1
1
1
1
1
k
T
k
k
k
T
k
k
T
k
k
T
k
k
T
k
KB
k
g
d
g
g
g
g
d
g
d
y
d
(10)
G
ha
n
b
a
r
i
(G
A
A
A
)
s
ugge
s
t
e
d
a
n
i
m
po
rt
a
nt
n
o
nl
i
n
e
a
r
S
C
G
a
pp
r
o
a
c
h
f
o
r
s
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l
v
i
n
g
o
pt
i
m
i
z
a
t
i
o
n
pr
o
b
l
e
m
s
[22]
.
T
h
e
i
r
s
y
s
t
e
m
i
s
b
a
s
e
d
o
n
a
h
y
b
r
i
d
s
pe
c
t
r
a
l
H
S
-
CG
s
y
s
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3].
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
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2502
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4752
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IS
S
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:
2502
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4752
In
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.
W
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1.
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R
EF
ER
EN
C
ES
[
1]
M
.
H
e
s
t
e
n
e
s
,
E
.
S
t
i
e
f
e
l
,
"
M
e
t
ho
ds
o
f
t
he
c
o
nj
ug
a
t
e
g
r
a
d
i
e
n
t
f
o
r
s
o
l
v
i
ng
a
l
i
n
e
a
r
s
y
s
t
e
m
"
,
J
our
nal
of
R
e
s
e
ar
c
h
o
f
t
he
N
at
i
ona
l
B
ur
e
au
of
S
t
an
dar
ds
,
v
o
l
.
49
,
409
-
436
,
195
2.
[
2]
R
.
F
l
e
t
c
he
r
a
nd
G
.
R
e
e
v
e
s
,
"
F
unc
t
i
o
n
M
i
n
i
m
i
z
a
t
i
o
n
by
G
r
a
d
i
e
nt
s
",
C
om
put
e
r
J
o
ur
na
l
,
v
o
l
.
7,
1
49
-
154
,
1964
.
[
3]
B
.
H
a
s
s
a
n
,
"
A
ne
w
c
l
a
s
s
o
f
B
F
G
S
upda
t
i
ng
f
o
r
m
ul
a
ba
s
e
d
o
n
t
he
ne
w
Q
ua
s
i
-
N
e
w
t
o
n
e
qu
a
t
i
o
n
"
,
I
nd
one
s
i
a
n
J
ou
r
na
l
of
E
l
e
c
t
r
i
c
a
l
E
ngi
ne
e
r
i
ng
and
C
o
m
p
ut
e
r
Sc
i
e
nc
e
(
I
J
E
E
C
S)
,
v
o
l
.
13
,
no
.
3
,
pp
.
945
-
95
3,
20
19
.
[
4]
B
.
H
a
s
s
a
n
,
"
A
ne
w
f
o
r
m
ul
a
f
o
r
c
o
nj
ug
a
t
e
pa
r
a
m
e
t
e
r
c
o
m
put
a
t
i
o
n
ba
s
e
d
o
n
t
he
qu
a
d
r
a
t
i
c
f
o
r
m
"
,
I
ndone
s
i
an
J
our
na
l
of
E
l
e
c
t
r
i
c
a
l
E
ngi
ne
e
r
i
ng
and
C
om
p
ut
e
r
Sc
i
e
nc
e
(
I
J
E
E
C
S)
,
v
o
l
.
13
,
no
.
3
,
pp
.
954
-
96
1
,
20
19
.
[
5]
E
.
P
o
l
a
k
,
a
nd
G
.
R
i
b
i
è
r
e
,
"
N
o
t
e
S
ur
l
a
C
o
nv
e
r
g
e
nc
e
de
D
i
r
e
c
t
i
o
ns
C
o
nj
ug
ué
e
"
,
R
e
v
.
F
r
anc
a
i
s
e
I
n
f
o
r
m
at
R
e
c
he
r
c
he
O
pe
r
at
i
ona
l
l
y
,
3
e
A
nné
e
,
v
o
l
.
16
,
35
-
43
,
1969
.
[
6]
R
.
F
l
e
t
c
he
r
,
"
P
r
a
c
t
i
c
a
l
M
e
t
ho
ds
o
f
O
pt
i
m
i
z
a
t
i
o
n
U
nc
o
ns
t
r
a
i
ne
d
O
pt
i
m
i
z
a
t
i
o
n
"
,
J
o
hn
W
i
l
e
y
&
Son
s
,
N
e
w
Y
o
r
k,
U
S
A
,
1987
.
[
7]
P
.
W
o
l
f
e
,
"
C
o
nv
e
r
g
e
nc
e
C
o
ndi
t
i
o
ns
f
o
r
A
s
c
e
nt
M
e
t
ho
ds
",
SI
A
M
R
e
v
i
e
w
,
v
o
l
.
11
,
226
-
23
5,
19
69
.
[
8]
H
.
Z
ha
ng
,
a
nd
W
.
H
a
g
e
r
,
"
A
l
go
r
i
t
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