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b
al
co
n
v
er
g
e
n
ce
p
r
o
p
er
ties
.
Fin
all
y
,
co
n
cl
u
s
io
n
a
n
d
r
ec
o
m
m
en
d
atio
n
f
o
r
f
u
t
u
r
e
s
tu
d
y
ar
e
w
r
ap
p
ed
u
p
at
s
ec
tio
n
f
o
u
r
.
2.
NE
W
C
G
CO
E
F
F
I
CI
E
N
T
T
h
e
n
e
w
C
G
co
ef
f
icie
n
t
in
tr
o
d
u
ce
d
is
k
n
o
w
n
as
S
M
R
k
.
S
M
R
k
is
m
o
ti
v
at
ed
m
ai
n
l
y
f
r
o
m
[
7
]
w
h
er
e
th
e
d
e
n
o
m
i
n
ato
r
is
r
etai
n
ed
as
s
a
m
e
a
s
i
n
(
1
0
)
.
W
h
ils
t,
t
h
e
n
o
m
in
ato
r
i
n
(
1
0
)
is
g
iv
e
n
a
s
1
k
k
T
k
g
g
g
w
h
ic
h
is
as
s
a
m
e
as
u
s
ed
in
(
5
)
an
d
(
7
)
.
Du
r
in
g
ex
p
a
n
s
io
n
,
t
h
e
n
o
m
in
ato
r
b
ec
o
m
es
1
k
T
k
k
T
k
g
g
g
g
w
h
ic
h
i
m
p
lies
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.
11
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
1
8
8
–
1
1
9
3
1190
1
2
k
T
k
k
g
g
g
.
C
h
o
o
s
i
n
g
t
h
e
r
ig
h
t
n
o
m
i
n
at
o
r
is
i
m
p
o
r
tan
t
d
u
e
to
its
r
o
le
as
a
r
estar
t
p
r
o
p
e
r
ty
i
n
av
o
id
in
g
p
r
o
b
lem
s
ass
o
ciate
d
w
it
h
j
am
m
in
g
,
[
1
3
-
1
4
]
.
P
r
ev
en
ti
n
g
an
y
n
e
g
ati
v
e
v
al
u
e,
m
o
d
if
ica
tio
n
s
h
a
s
b
ee
n
m
ad
e
[
1
5
]
; h
en
ce
th
e
n
e
w
C
G
co
ef
f
i
cien
t a
n
d
t
h
e
s
i
m
p
li
f
ied
v
er
s
io
n
ar
e
as f
o
llo
w
s
;
2
1
1
2
k
g
0,
m
a
x
k
k
T
k
S
M
R
k
d
g
g
(
1
1
)
B
ef
o
r
e
p
r
o
ce
e
d
s
w
it
h
m
o
r
e
d
etails s
tep
s
,
S
M
R
k
n
ee
d
s
to
b
e
s
i
m
p
li
f
i
ed
;
2
2
1
k
2
1
2
1
k
1
1
k
2
1
1
g
g
g
f
o
r
0
k
k
k
T
k
k
T
k
S
M
R
k
d
d
g
g
g
g
2
2
1
k
1
g
0
k
S
M
R
k
d
(
1
2
)
A
lg
o
r
ith
m
2
.
1
:
C
o
nju
g
a
te
Gra
d
ient M
etho
d
A
co
m
p
lete
al
g
o
r
it
h
m
o
f
C
G
m
et
h
o
d
co
u
ld
b
e
g
en
er
ated
as f
o
llo
w
s
:
Step
1
:
I
n
itializatio
n
.
Set
0
k
an
d
s
elec
t
n
x
0
,
0
0
g
d
,
if
0
0
g
,
s
to
p
.
Step
2
: B
ased
o
n
(
1
1
)
,
co
m
p
u
t
e
S
M
R
k
.
Step
3
:
C
o
m
p
u
te
s
ea
r
ch
d
ir
ec
tio
n
s
k
d
b
ased
o
n
(
3
)
.
I
f
k
g
,
th
en
s
to
p
.
Oth
er
w
i
s
e,
g
o
th
e
n
e
x
t step
.
Step
4
:
B
ased
o
n
(
4
)
,
s
o
lv
e
f
o
r
k
.
Step
5
:
Up
d
atin
g
n
e
w
i
n
i
tial
p
o
i
n
t
u
s
i
n
g
(
2
)
.
I
f
)
(
)
(
1
k
k
x
f
x
f
an
d
k
g
th
e
n
,
s
to
p
.
Ot
h
er
w
is
e
g
o
to
Step
3
w
it
h
1
k
k
.
3.
T
H
E
O
R
E
T
I
CA
L
ANA
L
YS
I
S
T
h
is
s
ec
tio
n
d
is
c
u
s
s
ed
an
d
an
al
y
s
ed
th
e
s
u
f
f
icie
n
t
d
escen
t
p
r
o
p
e
r
ty
f
o
r
th
e
n
e
w
co
e
f
f
ic
ien
t
u
n
d
er
s
tr
o
n
g
W
o
l
f
e
-
P
o
w
ell
li
n
e
s
ea
r
ch
d
ir
ec
tio
n
.
B
ef
o
r
e
p
r
o
ce
ed
,
let
ass
u
m
e
t
h
at
0
k
g
f
o
r
all
k
o
r
else,
th
e
s
tatio
n
ar
y
p
o
in
t
h
as
b
ee
n
f
o
u
n
d
.
Fo
r
an
y
iter
ati
v
e
m
et
h
o
d
to
b
e
g
lo
b
all
y
co
n
v
er
g
en
t,
it
i
s
i
m
p
o
r
ta
n
t
to
s
u
f
f
ic
e
its
d
escen
t p
r
o
p
er
t
y
,
th
at
i
s
;
0
k
T
k
d
g
.
3
.
1
.
Su
f
f
icient
Descent
P
ro
pert
y
B
ef
o
r
e
p
r
o
ce
e
d
,
let
ass
u
m
e
t
h
at
0
k
g
f
o
r
all
k
o
r
else,
th
e
s
tatio
n
ar
y
p
o
in
t h
as b
ee
n
f
o
u
n
d
.
Fo
r
an
y
iter
ativ
e
m
eth
o
d
to
b
e
g
lo
b
all
y
co
n
v
er
g
e
n
t,
it is
i
m
p
o
r
tan
t to
s
u
f
f
ice
its
d
esce
n
t p
r
o
p
er
ty
,
t
h
at
is
;
2
k
k
T
k
g
c
d
g
(
1
3
)
w
h
er
e
c
is
a
p
o
s
iti
v
e
co
n
s
ta
n
t,
is
cr
u
cial
to
en
s
u
r
e
t
h
e
g
lo
b
al
co
n
v
er
g
e
n
ce
s
o
f
t
h
e
n
o
n
lin
ea
r
co
n
j
u
g
ate
g
r
ad
ien
t
m
et
h
o
d
u
n
d
er
s
tr
o
n
g
W
o
lf
e
-
P
o
w
ell
li
n
e
s
ea
r
c
h
d
ir
ec
tio
n
[
1
6
]
.
Su
f
f
ic
ien
t
d
escen
t
p
r
o
p
er
ty
is
i
m
p
o
r
tan
t
to
s
h
o
w
t
h
at
t
h
e
f
u
n
ctio
n
)
(
x
f
ca
n
b
e
r
ed
u
ce
s
alo
n
g
t
h
e
s
ea
r
ch
d
ir
ec
ti
o
n
.
T
h
e
p
r
o
v
in
g
s
tep
s
b
elo
w
ar
e
m
o
d
i
f
ied
f
r
o
m
[
1
1
-
1
2
]
.
Th
eo
r
em
3
.
1
I
f
k
g
an
d
k
d
ar
e
g
en
er
ated
b
y
al
g
o
r
it
h
m
2
.
1
w
it
h
25
6
,
th
en
,
f
o
r
all
0
k
,
it b
e
co
m
e
s
;
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
Glo
b
a
l Co
n
ve
r
g
en
ce
o
f a
N
ew C
o
efficien
t No
n
lin
ier C
o
n
ju
g
a
te
Gra
d
ien
t M
eth
o
d
(
N
u
r
S
ya
r
a
fin
a
Mo
h
a
med
)
1191
3
5
k
k
d
g
(
1
4
)
P
r
o
o
f
T
h
e
p
r
o
v
in
g
s
tep
s
ar
e
p
er
f
o
r
m
ed
b
y
in
d
u
ctio
n
s
.
Fo
r
0
k
an
d
3
5
1
0
0
d
g
,
h
en
ce
(
1
4
)
h
o
ld
s
f
o
r
0
k
.
Su
p
p
o
s
e
f
o
r
s
o
m
e
0
k
,
(
1
4
)
h
o
ld
s
t
r
u
e.
R
ea
r
r
an
g
e
(
3
)
an
d
m
u
ltip
l
y
in
g
it
w
i
th
T
k
g
1
,
th
en
k
T
k
k
k
k
T
k
d
g
g
d
g
1
1
2
1
1
1
(
1
5
)
Fr
o
m
s
tr
o
n
g
W
o
lf
e
-
P
o
w
ell
co
n
d
itio
n
a
n
d
ab
s
o
lu
te
v
a
lu
e
s
p
r
o
p
er
ties
in
(
4
)
,
ex
p
r
ess
io
n
(
1
5
)
b
ec
o
m
es;
k
T
k
k
k
T
k
k
d
g
d
g
g
1
1
1
1
2
1
k
T
k
k
k
T
k
k
d
g
d
g
g
1
1
1
2
1
(
1
6
)
Sin
ce
,
0
1
S
MR
k
th
en
k
T
k
k
k
T
k
k
d
g
d
g
g
1
1
1
2
1
(
1
7
)
B
y
u
s
i
n
g
C
a
u
ch
y
i
n
eq
u
ali
ties
an
d
s
u
b
s
tit
u
tin
g
(
1
2
)
in
(
1
7
)
,
k
k
k
k
k
k
k
d
g
d
g
d
g
g
2
2
1
1
1
2
1
(
1
8
)
I
m
p
lies
;
k
k
k
k
k
k
d
g
g
d
g
g
2
1
1
1
2
1
(
1
9
)
A
p
p
l
y
in
g
t
h
e
in
d
u
c
tio
n
h
y
p
o
t
h
esi
s
in
(
1
4
)
,
2
1
1
1
2
1
3
5
k
k
k
k
g
d
g
g
1
1
2
1
)
3
5
1
(
k
k
k
d
g
g
)
5
3
(
3
1
1
k
k
d
g
(
20)
T
h
er
ef
o
r
e,
if
25
6
,
th
en
.
3
5
1
1
k
k
d
g
Hen
ce
,
(
1
4
)
is
tr
u
e
f
o
r
1
k
.
T
h
e
p
r
o
o
f
is
co
m
p
l
eted
.
3
.
2
.
G
lo
ba
l C
o
nv
er
g
ence
P
ro
pert
ies
T
h
e
f
o
llo
w
in
g
ass
u
m
p
tio
n
is
n
ee
d
ed
i
n
o
r
d
er
to
p
r
o
ce
ed
w
it
h
t
h
e
p
r
o
o
f
o
f
g
lo
b
al
co
n
v
er
g
en
ce
p
r
o
p
er
ties
.
T
h
e
p
r
o
o
f
m
o
d
i
f
ica
tio
n
s
ar
e
f
r
o
m
[
1
1
-
1
2
,
1
7
-
19]
A
s
s
u
mp
tio
n
4
.
1
1)
f
is
b
o
u
n
d
ed
b
elo
w
o
n
t
h
e
le
v
el
s
e
t
n
R
an
d
is
co
n
ti
n
u
o
u
s
a
n
d
d
if
f
er
en
tiab
le
i
n
a
n
ei
g
h
b
o
r
h
o
o
d
N
o
f
t
h
e
lev
el
s
et
)
(
)
(
|
0
x
f
x
f
R
x
n
at
t
h
e
i
n
itial p
o
in
t
0
x
.
2
)
T
h
e
g
r
ad
ien
t
)
(
x
g
is
L
ip
s
c
h
itz
co
n
ti
n
u
o
u
s
i
n
N
,
s
o
th
er
e
ex
is
t
s
a
co
n
s
ta
n
t
0
L
s
u
ch
t
h
at;
y
x
L
y
g
x
g
)
(
)
(
N
y
x
a
n
y
f
o
r
,
(
2
1
)
Fro
m
(
1
1
)
an
d
(
1
3
)
,
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.
11
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
1
8
8
–
1
1
9
3
1192
0
if
0
if
1
2
1
2
k
T
k
k
k
k
T
k
k
k
S
M
R
k
d
g
d
g
d
g
d
g
(
2
2
)
Th
eo
r
em
4
.
2
Su
p
p
o
s
e
th
at
Ass
u
m
p
tio
n
4
.
1
h
o
ld
s
.
C
o
n
s
id
er
an
y
C
G
m
et
h
o
d
in
th
e
f
o
r
m
o
f
(
2
)
an
d
(
3
)
w
h
er
e
k
is
o
b
tain
ed
f
r
o
m
(
4
)
.
I
f
th
e
d
esce
n
d
co
n
d
itio
n
h
o
ld
s
,
t
h
e
n
;
0
i
n
f
l
i
m
k
k
g
(
2
3
)
P
r
o
o
f
T
o
p
r
o
v
e
T
h
eo
r
em
4
.
2
,
co
n
tr
ad
ictio
n
m
e
th
o
d
is
u
s
ed
.
T
h
at
is
,
if
T
h
eo
r
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4
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8
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l
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o
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2
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Fro
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2
9
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,
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2
3
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h
o
ld
s
.
T
h
e
p
r
o
o
f
is
co
m
p
leted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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ac
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an
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Fo
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w
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w
it
h
t
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p
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p
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ctio
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f
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r
f
u
t
u
r
e
s
t
u
d
y
.
RE
F
E
R
E
NC
E
S
[1
]
Ha
m
iza
h
,
N.,
Riv
a
ie,
M
,
M
a
m
a
t,
M
.
(2
0
1
6
).
A
M
o
d
if
ied
Fo
rm
o
f
Co
n
j
u
g
a
te
Gr
a
d
ien
t
M
e
th
o
d
fo
r
Un
c
o
n
st
ra
i
n
e
d
Op
ti
miza
ti
o
n
Pro
b
lem
s
.
AIP
C
o
n
f
e
re
n
c
e
P
ro
c
e
e
d
i
n
g
s
,
1
7
3
9
,
0
2
0
0
7
6
.
[2
]
He
ste
n
e
s,
M
.
R,
S
t
ief
e
l,
E.
(1
9
6
2
).
M
e
th
o
d
o
f
Co
n
j
u
g
a
te
G
ra
d
ien
t
f
o
r
S
o
lv
in
g
L
in
e
a
r
Eq
u
a
ti
o
n
s.
J
.
Res
.
Na
t.
Bu
r
.
S
ta
n
d
,
4
9
:4
0
9
-
4
3
6
.
[3
]
F
letc
h
e
r,
R,
Re
e
v
e
s,
C.
(1
9
6
4
).
F
u
n
c
ti
o
n
m
in
im
iza
ti
o
n
b
y
c
o
n
ju
g
a
t
e
g
ra
d
ien
ts.
Co
mp
u
ta
ti
o
n
a
l
J
o
u
r
n
a
l
,
7
:1
4
9
-
1
5
4
.
[4
]
P
o
lak
,
E,
Rib
iere
,
G
.
(1
9
6
9
).
No
te
o
n
T
h
e
Co
n
v
e
rg
e
n
c
e
o
f
Co
n
j
u
g
a
te
Dire
c
ti
o
n
s.
Rev
.
Fra
n
c
a
ise
In
fo
rm
a
t
Rec
h
e
rc
h
e
Op
e
ra
ti
o
n
e
ll
e
,
3
E
An
n
e
e
,
1
6
:
3
5
-
4
3
.
[5
]
F
letc
h
e
r,
R.
(
1
9
8
7
)
.
Pra
c
ti
c
a
l
M
e
th
o
d
s
o
f
U
n
c
o
n
str
a
in
e
d
Op
t
imiza
ti
o
n
.
Ne
w
Yo
rk
:
J.
W
il
e
y
a
n
d
S
o
n
s
.
[6
]
Da
i,
Y.
H,
Yu
a
n
,
Y.
(2
0
0
0
).
A
No
n
li
n
e
a
r
Co
n
j
u
g
a
te
G
ra
d
ien
t
w
i
th
S
tr
o
n
g
G
lo
b
a
l
C
o
n
v
e
rg
e
n
c
e
P
ro
p
e
rti
e
s.
S
IAM
J
o
u
rn
a
l
Op
t
imiza
ti
o
n
,
1
0
:
1
7
7
-
1
8
2
.
[7
]
Riv
a
ie,
M
.
,
M
a
m
a
t,
M
.
,
J
u
n
e
,
L
.
W
,
M
o
h
d
,
I
.
(2
0
1
2
).
A
Ne
w
Clas
s
o
f
No
n
li
n
e
a
r
Co
n
ju
g
a
te
G
ra
d
ien
t
C
o
e
ff
icie
n
ts
W
it
h
G
lo
b
a
l
Co
n
v
e
rg
e
n
c
e
P
r
o
p
e
r
ti
e
s.
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
s
a
n
d
Co
mp
u
ta
ti
o
n
a
l
,
2
1
8
:
1
1
3
2
3
-
1
1
3
3
2
.
[8
]
Zo
u
te
n
d
ij
k
,
G
.
(1
9
7
0
).
No
n
li
n
e
a
r
p
r
o
g
ra
m
m
in
g
c
o
m
p
u
tatio
n
a
l
m
e
th
o
d
s.
J
.
Ab
a
d
ie
(
Ed
.
)
,
I
n
teg
e
r
a
n
d
No
n
li
n
e
a
r
Pro
g
ra
mm
i
ng
,
No
rt
h
-
Ho
ll
a
n
d
,
Am
ste
rd
a
m
,
3
7
–
86.
[9
]
P
o
w
e
ll
,
M
.
J.
D.
(1
9
8
4
).
N
o
n
-
c
o
n
v
e
x
min
imiza
ti
o
n
c
a
lc
u
la
t
i
o
n
s
a
n
d
t
h
e
c
o
n
j
u
g
a
te
g
r
a
d
ie
n
t
me
th
o
d
.
L
e
c
tu
re
n
o
tes
in
ma
t
h
e
ma
ti
c
s
,
1
0
6
6
:
1
2
2
-
1
4
1
.
B
e
rli
n
:
S
p
rin
g
e
r.
[1
0
]
Al
-
Ba
a
li
,
M
.
(1
9
8
5
).
De
sc
e
n
t
p
r
o
p
e
rty
a
n
d
g
lo
b
a
l
c
o
n
v
e
rg
e
n
c
e
o
f
F
letc
h
e
r
–
Re
e
v
e
s
m
e
th
o
d
w
it
h
in
e
x
a
c
t
li
n
e
se
a
rc
h
IM
A
.
J
o
u
rn
a
l
Nu
me
ric
a
l
A
n
a
lys
is
,
5:
1
2
1
-
1
2
4
.
[1
1
]
A
b
d
e
ra
h
m
a
n
,
A
.
A
.
,
M
a
m
a
t,
M
.
,
RIv
a
ie,
M
,
Om
e
r.
O.
(2
0
1
4
).
G
lo
b
a
l
C
o
n
v
e
rg
e
n
c
e
A
n
a
l
y
si
s
o
f
a
Ne
w
No
n
li
n
e
a
r
Co
n
j
u
g
a
te
G
ra
d
ien
t
Co
e
f
f
icie
n
t
w
it
h
S
tro
n
g
W
o
lf
e
L
in
e
S
e
a
rc
h
.
J
o
u
rn
a
l
o
f
Q
u
a
l
it
y
M
e
a
su
re
me
n
t
a
n
d
An
a
lys
is
,
1
0
(
1
):
7
5
-
8
5
.
[1
2
]
A
b
d
e
ra
h
m
a
n
,
A
.
A
.
,
M
a
m
a
t,
M
.
,
RIv
a
ie,
M
,
O
m
e
r.
O.
(
2
0
1
4
).
T
h
e
P
r
o
o
f
o
f
S
u
ff
icie
n
t
De
s
c
e
n
t
Co
n
d
it
io
n
f
o
r
a
Ne
w
Ty
p
e
o
f
Co
n
ju
g
a
te G
r
a
d
ien
t
M
e
th
o
d
s
.
A
IP
Co
n
fer
e
n
c
e
Pro
c
e
e
d
in
g
s
,
1
6
0
2
,
2
9
6
.
[1
3
]
Ha
ja
r,
N.,
M
a
m
a
t,
M
.
,
Riv
a
ie,
M
,
S
a
ll
e
h
,
Z.
(
2
0
1
5
)
.
A
Co
m
b
in
a
ti
o
n
o
f
P
o
lak
-
Rib
iere
a
n
d
He
ste
n
e
s
-
S
ti
e
fe
l
Co
e
ff
icie
n
t
in
Co
n
ju
g
a
te
G
ra
d
ien
t
M
e
th
o
d
f
o
r
Un
c
o
n
stra
in
e
d
Op
ti
m
iza
ti
o
n
.
Ap
p
li
e
d
M
a
th
e
ma
ti
c
a
l
S
c
ien
c
e
s,
9
(6
3
):3
1
3
1
-
3
1
4
2
.
[1
4
]
Riv
a
ie,
M
.
,
A
b
d
e
ra
h
m
a
n
,
A
.
,
M
a
m
a
t,
M
.
,
I
.
M
o
h
d
.
(2
0
1
4
).
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
j
u
g
a
te G
ra
d
ien
t
M
e
th
o
d
s
.
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
a
l
S
c
ien
c
e
s,
8
(1
):3
3
-
34.
[1
5
]
S
y
a
ra
f
in
a
,
N.
M
.
,
M
a
m
a
t,
M
,
Riv
a
ie,
M
.
(2
0
1
6
)
.
A
N
e
w
Co
e
ff
icie
n
t
o
f
Co
n
ju
g
a
te
G
ra
d
i
e
n
t
M
e
th
o
d
f
o
r
Un
c
o
n
stra
in
e
d
Op
t
im
iza
ti
o
n
.
J
u
r
n
a
l
T
e
k
n
o
l
o
g
i
.
7
8
:
6
-
4
,
1
3
1
-
1
3
6
.
[1
6
]
H
a
m
o
d
a
,
M
.
,
M
a
m
a
t,
M
.
,
Riv
a
ie,
M
,
S
a
ll
e
h
,
Z.
(
2
0
1
6
)
.
A
Co
n
j
u
g
a
te
G
r
a
d
ien
t
M
e
th
o
d
w
it
h
S
tr
o
n
g
W
o
lf
e
-
P
o
w
e
ll
L
in
e
S
e
a
rc
h
f
o
r
Un
c
o
n
stra
in
e
d
Op
ti
m
iza
ti
o
n
.
A
p
p
li
e
d
M
a
th
e
m
a
ti
c
a
l
S
c
ien
c
e
,
1
0
(
1
5
)
:
7
2
1
-
7
3
4
.
[1
7
]
Do
n
g
,
X
.
L
.
,
L
iu
,
H.
,
X
u
,
Y.
L
.
,
Ya
n
g
,
X
.
M
.
(2
0
1
5
).
S
o
m
e
L
in
e
a
r
Co
n
ju
g
a
te
G
ra
d
ien
t
M
e
th
o
d
s
w
it
h
S
u
f
f
i
c
ien
t
De
sc
e
n
t
Co
n
d
it
io
n
a
n
d
G
lo
b
a
l
Co
n
v
e
rg
e
n
c
e
.
Op
ti
miza
ti
o
n
L
e
tt
e
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[1
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1
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(1
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):
6
3
7
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-
6
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8
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.
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