I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
p
u
t
er
Science
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
,
p
p
.
1
6
4
3
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1
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4
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1
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1643
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ttp
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ee
cs.ia
esco
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e.
co
m
T
w
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v
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f
descent
co
njuga
te
g
ra
dient
m
et
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la
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stra
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m
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a
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A.
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a
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a
n
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De
p
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rtme
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f
M
a
th
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m
a
ti
c
s
,
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ll
e
g
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f
S
c
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s
,
Un
iv
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rsit
y
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Kirk
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q
2
De
p
a
rtme
n
t
o
f
M
a
th
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m
a
ti
c
s,
Co
ll
e
g
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o
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m
p
u
ters
S
c
ien
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e
s a
n
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M
a
th
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m
a
ti
c
s,
Un
iv
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rsit
y
o
f
M
o
su
l,
I
ra
q
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Mar
21
,
2
0
2
1
R
ev
i
s
ed
Ma
y
4
,
2021
A
cc
ep
ted
Ma
y
5
,
2021
T
h
e
c
o
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ju
g
a
te
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ra
d
ien
t
m
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th
o
d
s
a
re
n
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ted
t
o
b
e
e
x
c
e
e
d
in
g
ly
v
a
lu
a
b
le
f
o
r
so
lv
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g
larg
e
-
sc
a
le
u
n
c
o
n
stra
in
e
d
o
p
t
im
iza
ti
o
n
p
ro
b
lem
s
sin
c
e
it
n
e
e
d
n
'
t
th
e
sto
ra
g
e
o
f
m
a
tri
c
e
s.
M
o
stly
th
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p
a
ra
m
e
ter
c
o
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ju
g
a
te
is
t
h
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u
s
f
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r
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ju
g
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d
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t
m
e
th
o
d
s.
T
h
e
c
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rre
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t
p
a
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p
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p
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s
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w
m
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th
o
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p
a
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e
ter
o
f
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o
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g
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te
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ty
p
e
to
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lv
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lem
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o
f
larg
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s
c
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stra
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p
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m
iza
ti
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n
.
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ss
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a
p
p
ro
x
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a
ti
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in
a
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n
a
l
m
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tri
x
f
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th
e
b
a
sis
o
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se
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o
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d
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n
d
th
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d
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e
x
p
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n
sio
n
w
a
s
e
m
p
lo
y
e
d
in
t
h
is
stu
d
y
.
T
h
e
su
ff
icie
n
t
d
e
sc
e
n
t
p
r
o
p
e
rty
f
o
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th
e
p
r
o
p
o
se
d
a
lg
o
rit
h
m
a
re
p
ro
v
e
d
.
T
h
e
n
e
w
m
e
th
o
d
w
a
s
c
o
n
v
e
rg
e
d
g
lo
b
a
ll
y
.
T
h
is
n
e
w
a
lg
o
rit
h
m
is
f
o
u
n
d
to
b
e
c
o
m
p
e
ti
ti
v
e
to
th
e
a
lg
o
rit
h
m
o
f
f
letc
h
e
r
-
re
e
v
e
s
(F
R)
in
a
n
u
m
b
e
r
o
f
n
u
m
e
rica
l
e
x
p
e
ri
m
e
n
ts
.
K
ey
w
o
r
d
s
:
Glo
b
al
co
n
v
er
g
e
n
ce
p
r
o
p
er
ty
N
u
m
er
ical
ex
p
er
i
m
en
t
s
Un
co
n
s
tr
ain
ed
o
p
ti
m
iza
tio
n
s
Ver
s
io
n
s
o
f
c
o
n
j
u
g
ate
g
r
ad
ien
t
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
B
asi
m
A
.
Has
s
an
Dep
ar
t
m
en
t o
f
Ma
th
e
m
at
ics
C
o
lleg
e
o
f
C
o
m
p
u
ter
s
Scie
n
ce
s
an
d
Ma
th
e
m
atic
s
Un
i
v
er
s
it
y
o
f
Mo
s
u
l,
I
r
aq
E
m
ail:
b
asi
m
a
h
@
u
o
m
o
s
u
l.e
d
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
r
o
b
lem
o
f
u
n
co
n
s
tr
ai
n
ed
o
p
tim
iza
tio
n
i
s
g
e
n
er
all
y
f
o
r
m
u
lated
as:
{
(
)
|
∈
}
(
1
)
w
h
er
e
⥂
⥂
:
→
1
is
a
f
u
n
ctio
n
th
at
is
co
n
tin
u
o
u
s
ly
d
if
f
er
en
tiab
le.
Nu
m
er
o
u
s
f
am
o
u
s
tech
n
iq
u
es
ar
e
f
o
u
n
d
f
o
r
s
o
lv
in
g
(
1
)
;
h
o
w
ev
er
,
th
e
co
n
j
u
g
ate
g
r
ad
ien
t
(
C
G)
tech
n
iq
u
es
ar
e
th
e
m
ain
ly
ch
ar
ac
ter
ized
o
n
e
s
.
New
to
n
tech
n
iq
u
e
is
f
am
o
u
s
if
th
e
g
r
ad
ien
t
m
atr
ix
is
n
o
n
n
eg
ativ
e
d
ef
in
ite,
f
o
r
m
o
r
e
d
etails
s
ee
[
1
]
.
T
h
ese
CG
-
tech
n
iq
u
es
ar
e
in
th
e
v
ar
iety
o
f
iter
atio
n
s
k
n
o
w
n
b
y
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2
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w
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k
is
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th
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tain
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s
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r
ch
:
(
)
−
(
+
)
≥
−
(
3
)
(
+
)
≥
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
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J
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lec
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n
g
&
C
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m
p
Sci,
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
:
1
6
4
3
-
1
6
4
9
1644
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h
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<
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h
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k
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e
ar
e
ca
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lated
as:
0
=
−
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+
1
=
−
+
1
+
(
5
)
a
t
th
is
p
o
in
t
is
a
s
ca
lar
g
iv
en
as
th
e
p
ar
am
eter
o
f
co
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ate
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ad
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en
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A
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al
y
zin
g
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h
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ld
w
id
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G
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tec
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n
iq
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e
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n
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g
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n
ce
in
m
i
x
t
u
r
e
w
i
th
in
e
x
ac
t
tech
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iq
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es
o
f
li
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s
ea
r
ch
[
2
]
.
In
th
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tec
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n
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e
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f
q
u
a
s
i
-
Ne
w
to
n
(
QN)
,
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e
d
ir
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tio
n
o
f
s
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ch
is
ca
lc
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lated
u
s
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n
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an
ap
p
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x
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m
at
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o
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h
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ia
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atr
ix
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n
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er
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e.
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n
m
e
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lo
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s
(
5
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ch
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g
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y
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1
−
1
+
1
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7
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w
h
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y
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h
e
Hes
s
ia
n
m
a
tr
ix
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1
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p
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ated
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u
r
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g
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h
e
iter
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n
s.
Mo
r
e
d
etails
ca
n
b
e
f
o
u
n
d
in
[3
]
,
[
4
]
.
I
n
m
o
d
er
n
y
ea
r
s
,
a
d
iv
er
s
it
y
o
f
C
G
-
f
o
r
m
u
las
w
as
k
n
o
w
n
,
m
aj
o
r
ly
,
d
i
f
f
er
en
ce
s
ar
e
in
th
e
p
ar
am
eter
,
th
e
w
o
r
k
b
y
d
is
c
u
s
s
ed
d
etails
o
n
s
o
m
e
C
G
-
tec
h
n
i
q
u
s
w
it
h
s
p
ec
ial
e
m
p
h
a
s
is
o
n
t
h
eir
w
o
r
ld
w
id
e
co
n
v
er
g
e
n
ce
.
Fu
r
t
h
er
m
o
r
e,
th
e
d
esig
n
o
f
C
G
-
tec
h
n
iq
u
es
h
ad
b
ee
n
s
tu
d
ied
b
y
m
a
n
y
o
f
r
esear
ch
er
s
f
o
r
ar
ch
et
y
p
e
r
ef
er
to
[
5
]
-
[
1
0
]
.
I
n
th
is
p
ap
er
,
th
e
n
ew
p
r
o
p
o
s
ed
m
eth
o
d
is
s
o
lv
ed
b
y
s
ec
o
n
d
an
d
th
ir
d
-
o
r
d
er
T
ay
lo
r
-
s
er
ies.
T
h
e
s
u
b
s
eq
u
en
t
s
ec
tio
n
s
o
f
s
tu
d
y
ar
e
o
r
g
an
ized
in
th
is
w
ay
:
th
e
s
ec
o
n
d
s
ec
tio
n
p
r
esen
ts
th
e
o
u
tlin
es
o
f
th
e
n
ew
alg
o
r
ith
m
an
d
th
e
d
er
iv
in
g
a
n
ew
f
o
r
m
u
la
.
So
m
e
in
ter
esti
n
g
th
e
co
n
v
er
g
en
ce
an
aly
s
is
o
f
th
e
n
ew
alg
o
r
ith
m
p
r
esen
ted
in
th
e
th
ir
d
s
ec
tio
n
.
R
esu
lts
o
f
th
e
cu
r
r
en
t
n
u
m
er
ical
ex
p
er
im
en
ts
ar
e
p
r
esen
ted
in
th
e
f
o
u
r
th
s
ec
tio
n
b
y
u
s
in
g
th
e
test
p
r
o
b
lem
s
f
o
u
n
d
in
[
1
1
]
.
Fin
ally
,
th
e
f
if
th
s
ec
tio
n
p
r
es
en
ts
s
o
m
e
o
b
v
io
u
s
f
in
d
in
g
s
.
2.
A
NE
W
CO
NJ
U
G
A
T
E
G
R
ADIE
NT
M
E
T
H
O
D
T
h
is
s
ec
tio
n
d
e
v
elo
p
s
a
n
e
w
C
G
-
m
eth
o
d
o
n
t
h
e
b
asi
s
o
f
ap
p
r
o
x
i
m
ati
n
g
t
h
e
Hes
s
i
an
w
it
h
“
a
s
y
m
m
etr
ic
p
o
s
itiv
e
-
d
e
f
in
ite
m
atr
i
x
.
No
w
,
th
e
s
ec
o
n
d
an
d
th
ir
d
-
o
r
d
er
T
ay
lo
r
-
s
er
ies
ap
p
r
o
x
i
m
atio
n
i
s
e
m
p
lo
y
ed
to
at
th
e
p
o
in
t
ca
n
b
e
w
r
itte
n
as b
y
f
o
llo
w
in
g
t
h
e
s
a
m
e
ap
p
r
o
ac
h
es a
s
i
n
[
1
2
]
as:
(
)
=
(
+
1
)
−
+
1
+
1
2
+
1
,
=
+
1
−
+
1
+
1
2
+
1
+
1
6
+
1
(
8
)
w
h
er
e
+
1
is
th
e
ten
s
o
r
o
f
f
at
th
e
p
o
in
t
+
1
.
T
h
en
,
b
y
u
s
i
n
g
a
+
1
=
0
in
s
ec
o
n
d
-
o
r
d
er
T
ay
lo
r
-
s
er
ies,
th
e
n
e
x
t r
elatio
n
(
9
)
is
o
b
tain
ed
:
+
1
=
2
(
(
)
−
(
+
1
)
)
(
9
)
t
h
e
r
elatio
n
(
1
0
)
is
o
b
tain
ed
b
y
th
ir
d
-
o
r
d
er
T
ay
lo
r
-
s
er
ies ex
p
r
ess
io
n
s
:
+
1
=
+
6
(
−
+
1
)
+
3
(
+
1
+
)
(
1
0
)
t
h
e
s
t
e
p
s
i
z
e
i
s
d
et
e
r
m
in
e
d
b
y
m
an
y
a
lg
o
r
it
h
m
s
.
I
n
ex
a
c
t
l
in
e
s
e
a
r
ch
th
e
s
t
e
p
le
n
g
t
h
i
s
s
e
le
c
te
d
a
s
(
1
1
)
.
=
−
(
1
1
)
F
r
o
m
s
o
m
e
alg
eb
r
a,
th
e
(
1
2
)
is
o
b
tain
ed
:
+
1
=
(
)
−
(
+
1
)
−
2
,
+
1
=
1
2
+
3
(
−
+
1
)
+
3
2
+
1
+
(
1
2
)
b
y
(
1
2
)
,
th
e
(
1
3
)
is
d
er
iv
ed
an
d
d
en
o
te
b
y
+
1
an
d
as
f
o
llo
w
s
:
+
1
=
(
)
−
(
+
1
)
−
/
2
×
,
+
1
=
1
2
+
3
(
−
+
1
)
+
3
2
+
1
+
×
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
Tw
o
-
ve
r
s
io
n
s
o
f d
escen
t
co
n
ju
g
a
te
g
r
a
d
ien
t m
eth
o
d
s
fo
r
la
r
g
e
-
s
ca
le
…
(
Ha
w
r
a
z
N
.
Ja
b
b
a
r
)
1645
t
h
en
,
it c
an
b
e
w
r
itten
as:
+
1
=
−
(
(
)
−
(
+
1
)
−
2
)
+
1
,
+
1
=
−
(
1
2
+
3
(
−
+
1
)
+
3
2
+
1
+
)
+
1
(
1
4
)
b
y
u
s
e
th
e
co
n
j
u
g
ac
y
co
n
d
itio
n
+
1
=
0
d
u
e
to
th
e
co
n
j
u
g
ac
y
o
f
N
ew
to
n
d
ir
ec
tio
n
s
w
ith
ex
ac
t
lin
e
s
ea
r
ch
es
.
+
1
=
−
(
(
)
−
(
+
1
)
−
/
2
)
+
1
=
0
+
1
=
−
(
1
2
+
3
(
−
+
1
)
+
3
2
+
1
+
)
+
1
=
0
(
1
5
)
Sim
ilar
ly
,
b
y
u
s
in
g
C
G
m
eth
o
d
s
f
o
r
q
u
ad
r
atic
f
u
n
ctio
n
s
w
ith
ex
ac
t
lin
e
s
ea
r
ch
es,
f
o
r
m
u
la
(
1
6
)
is
o
b
tain
ed
:
+
1
=
−
+
1
+
=
0
(
1
6
)
f
r
o
m
(
1
5
)
an
d
(
1
6
)
,
th
e
(
1
7
a
an
d
b
)
is
d
er
iv
ed
as f
o
llo
w
s
:
−
(
(
)
−
(
+
1
)
−
/
2
)
+
1
=
−
+
1
+
−
(
1
/
2
+
3
(
−
+
1
)
+
3
/
2
+
1
+
)
+
1
=
−
+
1
+
(
1
7
a)
f
r
o
m
ab
o
v
e
eq
u
atio
n
,
w
e
g
et:
=
−
(
(
)
−
(
+
1
)
−
/
2
)
+
1
+
+
1
=
−
(
1
/
2
+
3
(
−
+
1
)
+
3
/
2
+
1
+
)
+
1
+
+
1
(
1
7
b
)
t
h
en
,
th
e
f
o
llo
w
in
g
eq
u
atio
n
s
ar
e
o
b
tain
ed
:
=
(
1
−
(
)
−
(
+
1
)
−
/
2
)
+
1
,
=
(
1
−
1
2
+
3
(
−
+
1
)
+
3
2
+
1
+
)
+
1
(1
8
)
p
u
ttin
g
(
1
8
)
in
(
5
)
,
w
e
o
b
tain
e
d
:
+
1
=
−
+
1
+
(
1
−
(
)
−
(
+
1
)
−
/
2
)
+
1
+
1
=
−
+
1
+
(
1
−
1
2
+
3
(
−
+
1
)
+
3
2
+
1
+
)
+
1
(
1
9
)
f
o
r
s
im
p
licity
,
eq
u
atio
n
(
1
9
)
is
ca
lled
b
y
m
eth
o
d
.
A
ls
o
,
ca
n
b
e
w
r
itten
in
th
is
w
ay
an
d
d
en
o
ted
b
y
an
d
:
=
1
(
−
1
‖
‖
2
)
+
1
,
=
1
(
−
2
‖
‖
2
)
+
1
w
h
er
e
,
1
=
(
)
2
‖
‖
2
[
∗
(
)
−
(
+
1
)
−
2
]
,
2
=
(
)
2
‖
‖
2
[
∗
1
2
+
3
(
−
+
1
)
+
3
2
+
1
+
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
22
,
No
.
3
,
J
u
n
e
2
0
2
1
:
1
6
4
3
-
1
6
4
9
1646
On
th
e
b
asis
o
f
ab
o
v
e
d
is
cu
s
s
io
n
,
th
i
s
s
ec
tio
n
d
escr
ib
es
th
e
alg
o
r
ith
m
f
r
a
m
e
o
f
t
h
is
s
tu
d
y
w
it
h
o
u
t
f
i
x
ed
lin
e
s
ea
r
c
h
in
t
h
i
s
w
a
y
.
Ne
w
a
l
g
o
r
ith
m
s
(
B
T
Q
an
d
B
T
C
a
lg
o
r
it
h
m
s
)
:
Step
1
:
Giv
e
1
∈
,
>
0
.
Se
t
1
=
−
1
,
=
1
.
If
‖
1
‖
≤
1
0
−
6
,
th
en
s
to
p
.
Step
2
:
C
o
m
p
u
te
s
atis
f
y
in
g
“
th
e
co
n
d
itio
n
s
(3
-
4)
.
Step
3
:
L
et
+
1
=
+
an
d
+
1
=
(
+
1
)
.
If
‖
+
1
‖
≤
1
0
−
6
,
th
en
s
to
p
.
Step
4
:
C
o
m
p
u
te
b
y
th
e
f
o
r
m
u
lae
(
1
2
)
th
en
g
en
er
ate
+
1
b
y
eq
u
atio
n
(
1
3
)
Step
5
:
Set
k
=
k
+
1
an
d
co
n
ti
n
u
e
w
i
th
s
teg
e
2
3.
CO
NVER
G
E
NT
A
NAL
YSI
S
T
h
e
f
o
llo
w
i
n
g
s
ec
tio
n
p
r
o
v
es
th
e
p
r
o
p
er
ty
o
f
g
lo
b
al
co
n
v
er
g
en
ce
o
f
n
e
w
m
eth
o
d
.
T
h
eo
r
em
3
.
1
d
em
o
n
s
tr
ate
s
th
a
t
th
e
d
ir
ec
tio
n
o
f
s
ea
r
c
h
in
al
g
o
r
it
h
m
s
is
c
o
n
tin
u
o
u
s
l
y
s
u
f
f
icie
n
t
d
esce
n
t
b
ased
o
n
n
o
lin
e
s
ea
r
ch
.
T
h
e
p
r
o
p
er
ty
o
f
s
u
f
f
i
cien
t
d
esce
n
t
is
o
n
e
o
f
t
h
e
i
m
p
o
r
ta
n
t
p
r
o
p
er
ties
o
f
th
e
all
co
n
j
u
g
ate
g
r
ad
ie
n
t
m
et
h
o
d
s
.
3
.
1
.
T
heo
re
m
L
et
,
,
+
1
∈
,
∈
an
d
=
1
(
−
‖
‖
2
)
+
1
,
w
h
er
e
∈
(
1
/
4
,
∞
)
.
I
f
≠
0
,
t
h
en
+
1
+
1
≤
−
[
1
−
1
/
4
]
‖
+
1
‖
2
.
P
r
o
o
f
:
Sin
ce
0
=
−
0
,
w
e
h
av
e
0
0
=
−
‖
0
‖
2
,
s
atis
f
y
in
g
(
6
)
.
T
h
r
o
u
g
h
m
u
ltip
ly
in
g
(
1
9
)
b
y
+
1
(
2
0
)
is
o
b
tain
ed
:
+
1
+
1
=
−
‖
+
1
‖
2
+
(
+
1
−
‖
‖
2
(
)
2
+
1
)
+
1
(
2
0
)
y
ield
in
g
+
1
+
1
=
(
+
1
)
(
+
1
)
(
)
−
‖
+
1
‖
2
(
)
2
−
‖
‖
2
(
+
1
)
2
(
)
2
(
2
1
)
T
h
e
in
eq
u
ality
≤
1
2
(
‖
‖
2
+
‖
‖
2
)
is
ap
p
lied
w
ith
=
1
(
)
+
1
an
d
=
(
+
1
)
,
w
h
er
e
∈
(
1
√
2
,
√
2
]
,
to
th
e
f
ir
s
t
ter
m
o
f
th
e
ab
o
v
e
eq
u
ality
,
th
e
(
2
3
)
is
o
b
tain
ed
:
(
+
1
)
(
+
1
)
(
)
≤
1
2
[
1
2
(
)
2
‖
+
1
‖
2
+
2
(
+
1
)
2
‖
‖
2
]
(
2
2
)
t
h
is
y
ield
s
,
+
1
+
1
≤
[
1
2
2
−
1
]
(
)
2
‖
+
1
‖
2
+
[
2
2
−
]
(
+
1
)
2
‖
‖
2
(
)
2
(
2
3
)
Fro
m
(
1
8
)
,
th
e
(
2
4
)
is
d
er
iv
ed
as f
o
llo
w
s
:
+
1
+
1
≤
[
1
2
2
−
1
]
‖
+
1
‖
2
≤
−
[
1
−
1
2
2
]
‖
+
1
‖
2
(
2
4
)
T
h
er
ef
o
r
e,
th
e
(
2
5
)
is
o
b
tain
ed
:
+
1
+
1
≤
−
[
1
−
1
4
]
‖
+
1
‖
2
(
2
5
)
C
o
n
s
eq
u
en
tly
,
it is
n
ec
ess
ar
y
to
h
av
e
A
s
s
u
m
p
tio
n
3
.
2
f
o
r
an
aly
zin
g
th
e
g
lo
b
al
co
n
v
er
g
en
ce
o
f
a
lg
o
r
ith
m
s
.
3
.
2
.
Ass
u
m
ptio
n
i.
T
h
e
lev
el
s
et
=
{
∈
|
(
)
≤
(
0
)
}
is
co
n
s
tr
ai
n
ed
.
ii.
I
n
a
n
u
m
b
er
o
f
ar
ea
s
,
“
an
d
,
(
)
”
a
r
e
co
n
tin
u
o
u
s
l
y
d
i
f
f
er
e
n
tiab
le
an
d
th
eir
g
r
ad
ie
n
t id
L
ip
s
c
h
itz
is
co
n
tin
u
o
u
s
,
i.e
.
,
a
co
n
s
tan
t
>
0
ex
is
ts
,
li
k
e
th
a
t
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
Tw
o
-
ve
r
s
io
n
s
o
f d
escen
t
co
n
ju
g
a
te
g
r
a
d
ien
t m
eth
o
d
s
fo
r
la
r
g
e
-
s
ca
le
…
(
Ha
w
r
a
z
N
.
Ja
b
b
a
r
)
1647
‖
(
)
−
(
)
‖
≤
‖
−
‖
,
∀
,
∈
(
2
6
)
Un
d
er
th
e
ab
o
v
e
ass
u
m
p
tio
n
s
o
n
,
”
a
co
n
s
tan
t
>
0
ex
is
ts
,
lik
e
th
at:
‖
+
1
‖
>
(
2
7
)
f
o
r
all
∈
.
Mo
r
e
d
etails
ca
n
b
e
f
o
u
n
d
in
[
1
3
]
v
er
if
ied
th
at
th
e
n
ex
t
g
en
er
al
r
esu
lt
is
ap
p
lied
to
an
y
C
G
m
eth
o
d
w
ith
s
tr
o
n
g
W
o
lf
e
lin
e
s
ea
r
ch
:
3
.
3
.
L
e
m
m
a
Su
p
p
o
s
in
g
th
at
ass
u
m
p
tio
n
s
(
i)
an
d
(
ii)
ar
e
h
eld
,
th
en
co
n
s
id
er
an
y
m
eth
o
d
o
f
co
n
j
u
g
ate
g
r
ad
ien
t
(
2
)
an
d
(
5
)
w
h
er
e
+
1
”
is
a
d
escen
t
d
ir
ec
tio
n
an
d
”
is
ac
h
iev
ed
b
y
th
e
s
tr
o
n
g
W
o
lf
e
lin
e
s
ea
r
ch
(
3
)
an
d
(
4
)
.
I
f
:
∑
1
‖
+
1
‖
2
=
∞
,
≥
0
(
2
8
)
t
h
en
,
→
∞
‖
+
1
‖
=
0
(
2
9
)
3
.
4
.
T
heo
re
m
Su
p
p
o
s
in
g
th
at
ass
u
m
p
tio
n
s
ar
e
h
eld
,
th
en
co
n
s
id
er
m
eth
o
d
s
(
2
)
an
d
(
5
)
,
w
h
er
e
is
a
d
escen
t
d
ir
ec
tio
n
w
ith
an
d
g
iv
en
b
y
(
1
8
)
,
an
d
k
is
f
o
u
n
d
b
y
th
e
W
o
lf
e
lin
e
s
ea
r
ch
.
I
f
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
u
n
if
o
r
m
ly
,
th
en
→
∞
‖
+
1
‖
=
0
.
”
‖
+
1
‖
=
‖
−
+
1
+
‖
≤
‖
+
1
‖
+
|
|
‖
‖
≤
‖
+
1
‖
+
‖
(
−
‖
‖
2
)
‖
‖
+
1
‖
‖
‖
‖
‖
‖
‖
≤
‖
+
1
‖
+
‖
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+
1
‖
+
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+
1
‖
‖
‖
2
‖
‖
‖
‖
‖
‖
‖
‖
‖
‖
‖
‖
≤
‖
+
1
‖
+
‖
‖
‖
+
1
‖
+
‖
+
1
‖
‖
‖
‖
‖
‖
‖
‖
‖
≤
[
1
+
1
+
]
‖
+
1
‖
≤
[
2
+
]
‖
+
1
‖
(
3
0
)
T
h
is
r
elatio
n
s
h
o
w
s
th
at
:
∑
1
‖
+
1
‖
2
≥
1
≥
(
1
2
+
)
1
∑
1
≥
1
=
∞
(
3
1
)
b
ased
o
n
L
e
m
m
a
1
,
→
∞
‖
+
1
‖
=
0
”
is
d
er
iv
ed
,
w
h
ic
h
eq
u
a
ls
“
→
∞
‖
+
1
‖
=
0
f
o
r
u
n
i
f
o
r
m
l
y
co
n
v
e
x
f
u
n
ctio
n
.
4.
NUM
E
RICAL
R
E
SU
L
T
S
T
h
is
s
ec
tio
n
ex
p
lai
n
s
s
o
m
e
n
u
m
er
ical
ex
p
er
i
m
en
t
s
co
n
d
u
cte
d
f
o
r
test
in
g
B
T
Q
an
d
B
T
C
a
l
g
o
r
ith
m
s
.
So
m
e
test
p
r
o
b
le
m
s
s
t
u
d
ied
b
y
A
n
d
r
ei
[
1
1
]
w
er
e
u
s
ed
in
t
h
i
s
s
t
u
d
y
(
s
ee
T
ab
le
1
)
to
an
aly
ze
th
e
ef
f
icie
n
c
y
o
f
th
e
n
e
w
f
o
r
m
u
la
f
o
r
m
ed
in
t
h
i
s
s
tu
d
y
i
n
co
m
p
ar
is
o
n
t
o
th
e
m
et
h
o
d
o
f
FR
.
C
o
m
p
ar
is
o
n
is
b
ased
o
n
iter
atio
n
s
n
u
m
b
er
(
NI
)
an
d
f
u
n
ct
io
n
ev
alu
atio
n
s
n
u
m
b
er
(
NF)
th
e
C
G
alg
o
r
ith
m
s
b
y
teep
est
d
esc
en
t
d
ir
ec
tio
n
s
.
I
n
all
C
G,
th
e
s
tep
len
g
t
h
is
y
ield
ed
b
y
W
o
lf
e
lin
e
s
ea
r
ch
w
i
th
=
0
.
001
an
d
=
0
.
9
,
an
d
th
e
ter
m
i
n
atio
n
co
n
d
itio
n
is
‖
+
1
‖
≤
1
0
−
6
.
So
m
e
n
o
ted
p
ap
er
s
ca
n
b
e
s
ee
[
1
4
]
-
[
2
5
]
.
T
ab
les
1
p
r
esen
t
lis
t
o
f
s
o
m
e
n
u
m
er
ical
r
e
s
u
l
ts
o
f
t
h
is
s
t
u
d
y
.
B
ased
o
n
th
e
cu
r
r
en
t
n
u
m
er
i
ca
l
r
esu
l
ts
,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
s
,
B
T
Q
a
n
d
B
T
C
,
h
av
e
m
in
i
m
u
m
n
u
m
b
er
s
o
f
iter
atio
n
s
,
r
estar
ts
a
n
d
f
u
n
ct
io
n
e
v
alu
a
tio
n
s
in
all
i
m
p
le
m
en
ted
test
p
r
o
b
lem
s
i
n
th
is
s
t
u
d
y
,
ex
ce
p
t
f
o
r
p
r
o
b
lem
s
7
an
d
1
0
,
w
h
er
e
th
e
FR
alg
o
r
ith
m
h
a
s
less
n
u
m
b
er
s
o
f
iter
atio
n
s
,
r
estar
t
s
an
d
f
u
n
ctio
n
ev
al
u
atio
n
s
a
g
ai
n
s
t
t
h
e
n
e
w
p
r
o
p
o
s
ed
B
T
Q
an
d
B
T
C
alg
o
r
ith
m
s
.
Gen
er
all
y
,
t
h
e
p
er
ce
n
tag
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
n
e
w
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
B
T
Q
an
d
B
T
C
ca
n
b
e
co
m
p
u
ted
as
co
m
p
ar
ed
to
th
e
s
ta
n
d
ar
d
FR
a
lg
o
r
ith
m
f
o
r
th
e
g
e
n
er
al
T
o
o
ls
NI
,
NR
an
d
NF
s
h
o
w
n
i
n
T
ab
le
2
.
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3
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J
u
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2
0
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1
:
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6
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1
6
4
9
1648
T
ab
le
1
.
C
o
m
p
ar
is
o
n
o
f
FR
a
n
d
n
e
w
al
g
o
r
ith
m
s
(
B
T
Q
an
d
B
T
C
)
w
i
th
n
=1
0
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an
d
n
=1
0
0
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,
t
est f
u
n
ctio
n
P
.
N
o
n
F
R
a
l
g
o
r
i
t
h
m
B
T
Q
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l
g
o
r
i
t
h
m
B
T
C
a
l
g
o
r
i
t
h
m
NI
NR
NF
NI
NR
NF
1
1
0
0
47
93
38
84
39
82
1
0
0
0
78
1
3
1
37
87
33
75
2
1
0
0
43
88
43
95
45
1
0
0
1
0
0
0
46
92
40
87
37
79
3
1
0
0
32
52
15
30
13
25
1
0
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22
42
24
47
16
32
4
1
0
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25
43
23
45
22
44
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0
0
0
46
7
4
1
30
2
0
4
29
52
5
1
0
0
37
67
39
60
43
63
1
0
0
0
73
1
1
5
66
1
1
0
63
98
6
1
0
0
15
31
11
23
9
19
1
0
0
0
8
17
8
17
7
15
7
1
0
0
89
1
7
4
75
1
6
5
73
1
6
0
1
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1
1
72
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5
5
61
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3
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40
79
31
60
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84
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3
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30
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65
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0
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1
1
6
37
87
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85
10
1
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2
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92
1
4
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1
5
1
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3
7
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3
4
5
5
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7
4
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6
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30
56
26
47
1
0
0
0
98
1
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6
7
33
57
55
8
3
7
12
1
0
0
49
80
10
19
17
32
1
0
0
0
1
2
9
1
6
6
12
24
14
27
13
1
0
0
12
25
11
23
10
21
1
0
0
0
11
23
11
23
10
21
14
1
0
0
1
2
2
1
5
6
14
28
11
20
1
0
0
0
1
3
0
1
6
6
15
29
15
27
15
1
0
0
1
1
2
1
4
7
43
66
34
54
1
0
0
0
1
1
0
1
4
5
40
60
38
60
T
o
t
a
l
2
1
5
7
7
0
9
0
1
3
4
3
2
6
6
6
1
1
9
9
2
9
7
2
T
ab
le
2
.
R
elativ
e
ef
f
icie
n
c
y
o
f
th
e
n
e
w
al
g
o
r
ith
m
s
FR
a
l
g
o
r
i
t
h
m
B
T
Q
a
l
g
o
r
i
t
h
m
B
T
C
a
l
g
o
r
i
t
h
m
NI
1
0
0
%
6
2
.
2
6
%
5
5
.
5
8
%
NF
1
0
0
%
3
7
.
6
0
%
4
1
.
9
1
%
P
r
o
b
lem
s
n
u
m
b
er
s
i
n
d
icato
r
(
T
ab
le
1
)
:
1
)
is
th
e
e
x
ten
d
ed
R
o
s
en
b
r
o
ck
,
2
)
is
th
e
e
x
ten
d
e
d
W
h
ite
&
Ho
ls
t,
3
)
is
th
e
e
x
ten
d
ed
B
ea
l
e,
4
)
is
th
e
g
en
er
alize
d
tr
id
iag
o
n
al
1
,
5
)
is
th
e
g
en
er
alize
d
tr
id
iag
o
n
al
2
,
6
)
is
th
e
e
x
ten
d
ed
P
SC
1
,
7
)
is
t
h
e
e
x
te
n
d
ed
Ma
r
ato
s
,
8
)
is
th
e
e
x
ten
d
ed
W
o
o
d
,
9
)
is
th
e
e
x
ten
d
ed
q
u
ad
r
atic
p
en
alt
y
QP
2
,
1
0
)
is
th
e
p
ar
tial
p
er
t
u
r
b
ed
q
u
ad
r
atic
,
1
1
)
is
th
e
E
DE
NS
C
H
(
C
UT
E
)
,
1
2
)
is
th
e
DE
NSC
HN
C
(
C
UT
E
)
,
1
3
)
is
th
e
DE
NSC
HNB
(
C
UT
E
)
,
1
4
)
is
th
e
ex
te
n
d
ed
b
lo
ck
-
d
iag
o
n
al
B
D2
,
an
d
15
)
is
th
e
g
en
er
alize
d
q
u
ar
tic
GQ2
.
Fu
ll d
etails o
f
th
e
s
e
test
p
r
o
b
lem
s
ca
n
b
e
f
o
u
n
d
in
An
d
r
ie
[
1
1
]
.
5.
CO
NCLU
SI
O
NS
P
r
a
c
t
i
c
a
l
l
y
,
w
h
e
n
t
h
e
c
o
m
p
l
e
x
i
t
y
a
n
d
s
i
z
e
o
f
t
h
e
t
e
s
t
p
r
o
b
l
e
m
i
n
c
r
e
a
s
e
,
g
r
e
a
t
e
r
i
m
p
r
o
v
e
m
e
n
t
s
c
o
u
l
d
b
e
r
e
a
l
i
z
e
d
b
y
t
h
e
n
ew
a
l
g
o
r
i
t
h
m
s
b
e
c
a
u
s
e
t
h
e
n
e
w
p
r
o
p
o
s
e
d
a
l
g
o
r
i
t
h
m
i
s
m
o
r
e
s
t
a
b
l
e
a
n
d
a
l
w
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s
p
r
e
s
e
r
v
e
s
t
h
e
d
e
s
c
e
n
t
s
e
a
r
c
h
d
i
r
e
c
t
i
o
n
s
.
O
u
r
r
e
p
o
r
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e
d
r
e
s
u
l
t
s
s
h
o
w
e
d
t
h
a
t
t
h
e
p
r
o
p
o
s
e
d
m
e
t
h
o
d
s
a
r
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e
f
f
i
c
i
e
n
t
f
o
r
s
o
l
v
i
n
g
l
a
r
g
e
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s
c
a
l
c
u
n
c
o
n
s
t
r
a
i
n
e
d
o
p
t
i
m
i
z
a
t
i
o
n
.
G
e
n
e
r
a
l
l
y
,
t
h
e
p
e
r
c
e
n
t
a
g
e
p
e
r
f
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m
a
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c
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o
f
t
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n
ew
p
r
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p
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e
d
a
l
g
o
r
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t
h
m
s
B
T
Q
a
n
d
B
T
C
c
a
n
b
e
c
o
m
p
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t
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d
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s
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t
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t
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d
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r
d
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R
a
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t
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e
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e
r
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l
t
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o
l
s
N
I
,
N
R
a
n
d
N
F
.
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NO
WL
E
D
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E
NT
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h
e
au
th
o
r
s
ar
e
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er
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f
u
l
to
t
h
e
U
n
i
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it
y
o
f
Mo
s
u
l/
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o
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o
f
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ter
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th
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m
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tics
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n
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Un
i
v
er
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t
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f
Kir
k
u
k
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e
o
f
Scie
n
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es
f
o
r
th
eir
p
r
o
v
id
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f
ac
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ie
s
,
w
h
ic
h
h
elp
ed
to
i
m
p
r
o
v
e
th
e
q
u
alit
y
o
f
t
h
is
w
o
r
k
”.
RE
F
E
R
E
NC
E
[1
]
M
o
h
d
R
.
,
A
b
d
e
lr
h
a
m
a
n
A
.
,
M
u
sta
fa
M
.
,
a
n
d
Ism
a
il
M
.
,
“
T
h
e
Co
n
v
e
rg
e
n
c
e
P
ro
p
e
rti
e
s
o
f
a
Ne
w
Ty
p
e
o
f
Co
n
ju
g
a
te
G
ra
d
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t
M
e
th
o
d
s,”
Ap
p
li
e
d
M
a
t
h
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ma
ti
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1649
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d
Qin
N,
“
T
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stin
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ra
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iza
ti
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,
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o
u
rn
a
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[3
]
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a
h
J
.
L
.
a
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d
M
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k
A
.
H
.
,
“
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im
it
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B
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m
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li
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p
ti
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iza
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n
,
”
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a
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s J
o
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rn
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[4
]
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li
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A
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H
.
,
W
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J
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L
.
,
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n
d
M
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.
,
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BF
G
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,
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IKA
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1
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[5
]
M
a
g
n
u
s
R.
H
.
a
n
d
E
d
u
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r
d
S
.
,
“
M
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lv
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li
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e
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m
s,”
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o
u
rn
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o
f
Res
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e
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ti
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.
[6
]
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F
.
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d
C.
M
.
Re
e
v
e
s,
“
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m
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ti
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ra
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[7
]
Ba
si
m
A
.
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ss
an
,
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m
e
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d
M
.
S
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iq
,
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A
No
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ra
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,
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[8
]
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si
m
A
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Clas
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o
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,
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[9
]
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.
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0
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rry
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.
,
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ra
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m
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.
[1
1
]
A
n
d
rie
N,
“
A
n
Un
c
o
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stra
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d
O
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iza
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T
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ll
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,
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1
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p
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4
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[1
2
]
Zh
a
n
g
J
.
a
n
d
X
u
C
.
,
“
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r
o
p
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s
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d
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rica
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o
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m
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f
q
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a
si
-
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to
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m
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th
o
d
s
w
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to
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q
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ti
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n
s,
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o
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s
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3
-
5.
[1
3
]
Da
i
Y.,
Ha
n
J.,
L
iu
G
.
,
S
u
n
D.
,
Yin
H.,
a
n
d
Y
u
a
n
Y.
,
“
Co
n
v
e
rg
e
n
c
e
p
ro
p
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e
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f
n
o
n
li
n
e
a
r
c
o
n
ju
g
a
te
g
ra
d
ien
t
m
e
th
o
d
s,”
S
IAM
J
o
u
r
n
a
l
o
n
Op
ti
miza
ti
o
n
,
v
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l
.
1
0
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2
6
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3
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2
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8
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4
3
.
[1
4
]
W
u
C.
a
n
d
C
h
e
n
G.
,
“
Ne
w
t
y
p
e
o
f
c
o
n
ju
g
a
te
g
ra
d
ien
t
a
lg
o
rit
h
m
s
f
o
r
u
n
c
o
n
stra
i
n
e
d
o
p
ti
m
iza
ti
o
n
p
ro
b
lem
s,”
in
J
o
u
rn
a
l
o
f
S
y
ste
ms
E
n
g
i
n
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rin
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.
[1
5
]
A
.
A
lh
a
w
a
ra
t
a
n
d
Z
.
S
a
ll
e
h
,
“
M
o
d
if
ic
a
ti
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o
f
No
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li
n
e
a
r
Co
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j
u
g
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te G
ra
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M
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it
h
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a
k
W
o
lf
e
-
P
o
w
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ll
L
in
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a
rc
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,
”
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stra
c
t
a
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d
A
p
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8
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3
4
.
[1
6
]
Ba
si
m
A
.
Ha
ss
a
n
a
n
d
M
o
h
a
m
m
e
d
W
.
T
a
h
a
,
“
A
Ne
w
V
a
rian
ts
o
f
Qu
a
si
-
Ne
w
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E
q
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ti
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Ba
se
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Qu
a
d
ra
ti
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F
u
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c
ti
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n
f
o
r
Un
c
o
n
stra
i
n
e
d
O
p
ti
m
iz
a
ti
o
n
,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
E
n
g
i
n
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rin
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n
d
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o
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ter
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e
,
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l.
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9
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.
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0
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.
[1
7
]
Zah
ra
K.
a
n
d
A
li
A
.
,
“
A
n
e
w
m
o
d
if
ied
sc
a
led
c
o
n
j
u
g
a
te
g
ra
d
ien
t
m
e
th
o
d
f
o
r
larg
e
-
sc
a
le
u
n
c
o
n
stra
i
n
e
d
o
p
ti
m
iza
ti
o
n
w
it
h
non
-
c
o
n
v
e
x
o
b
jec
ti
v
e
f
u
n
c
ti
o
n
,
”
O
p
ti
miza
ti
o
n
M
e
th
o
d
s a
n
d
S
o
ft
wa
re
,
v
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l
.
3
4
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o
.
4
,
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p
.
7
8
3
-
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,
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0
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8
.
[1
8
]
Ba
si
m
A
.
Ha
ss
a
n
,
“
A
G
lo
b
a
ll
y
Co
n
v
e
rg
e
n
c
e
S
p
e
c
t
ra
l
Co
n
ju
g
a
te
G
ra
d
ien
t
M
e
th
o
d
f
o
r
S
o
lv
in
g
Un
c
o
n
stra
in
e
d
Op
ti
m
iza
ti
o
n
P
r
o
b
lem
s
,
”
AL
-
Ra
fi
d
a
i
n
J
o
u
rn
a
l
o
f
C
o
mp
u
ter
S
c
ien
c
e
s
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n
d
M
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t
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ti
c
s
,
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l.
1
0
,
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o
.
4
,
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2
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,
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9
9
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j.
2
0
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3
.
1
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3
5
4
3
.
[1
9
]
S
a
m
a
n
B.
K.
,
“
A
n
e
ig
e
n
v
a
lu
e
stu
d
y
o
n
th
e
s
u
f
f
i
c
ien
t
d
e
sc
e
n
t
p
ro
p
e
rty
o
f
a
m
o
d
if
ied
P
o
lak
-
Rib
i
-
P
o
lak
c
o
n
j
u
g
a
te
g
ra
d
ien
t
m
e
th
o
d
,
”
Bu
ll
e
ti
n
o
f
th
e
Ira
n
ia
n
M
a
t
h
e
ma
ti
c
a
l
S
o
c
iety
,
v
o
l.
4
0
,
n
o
.
1
,
p
p
.
2
3
5
-
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4
2
.
[2
0
]
Ya
b
e
H.
a
n
d
S
a
k
a
iwa
N
.
,
“
A
n
e
w
n
o
n
li
n
e
a
r
c
o
n
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u
g
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te
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ra
d
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t
m
e
t
h
o
d
f
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r
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n
c
o
n
stra
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Am
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