Method of alternating projections for the general absolute value equation
A novel approach for solving the general absolute value equation A x + B | x | = c where A , B ∈ I R m × n and c ∈ I R m is presented. We reformulate the equation as a nonconvex feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternatin...
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| Vydané v: | Journal of fixed point theory and applications Ročník 25; číslo 1 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Springer International Publishing
01.02.2023
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| ISSN: | 1661-7738, 1661-7746 |
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| Abstract | A novel approach for solving the general absolute value equation
A
x
+
B
|
x
|
=
c
where
A
,
B
∈
I
R
m
×
n
and
c
∈
I
R
m
is presented. We reformulate the equation as a nonconvex feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternating projections map is characterized under nondegeneracy conditions on
A
and
B
. Furthermore, we prove local linear convergence of the algorithm. Unlike most of the existing approaches in the literature, the algorithm presented here is capable of handling problems with
m
≠
n
, both theoretically and numerically. |
|---|---|
| AbstractList | A novel approach for solving the general absolute value equation
A
x
+
B
|
x
|
=
c
where
A
,
B
∈
I
R
m
×
n
and
c
∈
I
R
m
is presented. We reformulate the equation as a nonconvex feasibility problem which we solve via the method of alternating projections (MAP). The fixed points set of the alternating projections map is characterized under nondegeneracy conditions on
A
and
B
. Furthermore, we prove local linear convergence of the algorithm. Unlike most of the existing approaches in the literature, the algorithm presented here is capable of handling problems with
m
≠
n
, both theoretically and numerically. |
| ArticleNumber | 39 |
| Author | Chen, Jein-Shan Alcantara, Jan Harold Tam, Matthew K. |
| Author_xml | – sequence: 1 givenname: Jan Harold surname: Alcantara fullname: Alcantara, Jan Harold organization: Institute of Statistical Sciences – sequence: 2 givenname: Jein-Shan orcidid: 0000-0002-4596-9419 surname: Chen fullname: Chen, Jein-Shan email: jschen@math.ntnu.edu.tw organization: Department of Mathematics, National Taiwan Normal University – sequence: 3 givenname: Matthew K. surname: Tam fullname: Tam, Matthew K. organization: School of Mathematics and Statistics, The University of Melbourne |
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| Snippet | A novel approach for solving the general absolute value equation
A
x
+
B
|
x
|
=
c
where
A
,
B
∈
I
R
m
×
n
and
c
∈
I
R
m
is presented. We reformulate the... |
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| SubjectTerms | Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics |
| Title | Method of alternating projections for the general absolute value equation |
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