Inertial proximal alternating minimization for nonconvex and nonsmooth problems
In this paper, we study the minimization problem of the type L ( x , y ) = f ( x ) + R ( x , y ) + g ( y ) , where f and g are both nonconvex nonsmooth functions, and R is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the co...
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| Vydané v: | Journal of inequalities and applications Ročník 2017; číslo 1; s. 232 - 13 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cham
Springer International Publishing
2017
Springer Nature B.V SpringerOpen |
| Predmet: | |
| ISSN: | 1029-242X, 1025-5834, 1029-242X |
| On-line prístup: | Získať plný text |
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| Shrnutí: | In this paper, we study the minimization problem of the type
L
(
x
,
y
)
=
f
(
x
)
+
R
(
x
,
y
)
+
g
(
y
)
, where
f
and
g
are both nonconvex nonsmooth functions, and
R
is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the convergence by constructing a key function
H
that guarantees a sufficient decrease property of the iterates. In fact, we prove that if
H
satisfies the Kurdyka-Lojasiewicz inequality, then every bounded sequence generated by the algorithm converges strongly to a critical point of
L
. |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
| ISSN: | 1029-242X 1025-5834 1029-242X |
| DOI: | 10.1186/s13660-017-1504-y |