An iterative method for solving split minimization problem in Banach space with applications
Закрыть
Conţinutul numărului revistei
Articolul precedent
Articolul urmator
514 15
Ultima descărcare din IBN:
2023-01-28 01:14
Căutarea după subiecte
similare conform CZU
517.5+517.9 (7)
Анализ (301)
Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (243)
SM ISO690:2012
JOLAOSO, Lateef Olakunle, OGBUISI, Ferdinard Udochukwu, MEWOMO, Oluwatosin Temitope. An iterative method for solving split minimization problem in Banach space with applications. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2021, nr. 1-2(95-96), pp. 3-30. ISSN 1024-7696.
EXPORT metadate:
Google Scholar
Crossref
CERIF

DataCite
Dublin Core
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1-2(95-96) / 2021 / ISSN 1024-7696 /ISSNe 2587-4322

An iterative method for solving split minimization problem in Banach space with applications

CZU: 517.5+517.9
MSC 2010: 47H06, 47H09, 49J53, 65K10.

Pag. 3-30

Jolaoso Lateef Olakunle1, Ogbuisi Ferdinard Udochukwu12, Mewomo Oluwatosin Temitope1
 
1 University of KwaZulu-Natal,
2 DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)
 
 
Disponibil în IBN: 3 decembrie 2021


Rezumat

The purpose of this paper is to study an approximation method for finding a solution of the split minimization problem which is also a fixed point of a right Bregman strongly nonexpansive mapping in p-uniformly convex real Banach spaces which are also uniformly smooth. We introduce a new iterative algorithm with a new choice of stepsize such that its implementation does not require a prior knowledge of the operator norm. Using the Bregman distance technique, we prove a strong convergence theorem for the sequence generated by our algorithm. Further, we applied our result to the approximation of solution of inverse problem arising in signal processing and give a numerical example to show how the sequence values are affected by the number of iterations. Our result in this paper extends and complements many recent results in literature.

Cuvinte-cheie
split feasibility problems, split minimization problems, proximal operators, fixed point problems, inverse problems, Bregman distance, soft thresholding, Banach spaces

Cerif XML Export

<?xml version='1.0' encoding='utf-8'?>
<CERIF xmlns='urn:xmlns:org:eurocris:cerif-1.5-1' xsi:schemaLocation='urn:xmlns:org:eurocris:cerif-1.5-1 http://www.eurocris.org/Uploads/Web%20pages/CERIF-1.5/CERIF_1.5_1.xsd' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' release='1.5' date='2012-10-07' sourceDatabase='Output Profile'>
<cfResPubl>
<cfResPublId>ibn-ResPubl-143913</cfResPublId>
<cfResPublDate>2021-12-03</cfResPublDate>
<cfVol>95-96</cfVol>
<cfIssue>1-2</cfIssue>
<cfStartPage>3</cfStartPage>
<cfISSN>1024-7696</cfISSN>
<cfURI>https://ibn.idsi.md/ro/vizualizare_articol/143913</cfURI>
<cfTitle cfLangCode='EN' cfTrans='o'>An iterative method for solving split minimization problem in Banach space with applications</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>split feasibility problems; split minimization problems; proximal operators; fixed point problems; inverse problems; Bregman distance; soft
thresholding; Banach spaces</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>The purpose of this paper is to study an approximation method for finding a solution of the split minimization problem which is also a fixed point of a right Bregman strongly nonexpansive mapping in p-uniformly convex real Banach spaces which are also uniformly smooth. We introduce a new iterative algorithm with a new choice of stepsize such that its implementation does not require a prior knowledge of the operator norm. Using the Bregman distance technique, we prove a strong convergence theorem for the sequence generated by our algorithm. Further, we applied our result to the approximation of solution of inverse problem arising in signal processing and give a numerical example to show how the sequence values are affected by the number of iterations. Our result in this paper extends and complements many recent results in literature.</p></cfAbstr>
<cfResPubl_Class>
<cfClassId>eda2d9e9-34c5-11e1-b86c-0800200c9a66</cfClassId>
<cfClassSchemeId>759af938-34ae-11e1-b86c-0800200c9a66</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfResPubl_Class>
<cfClassId>e601872f-4b7e-4d88-929f-7df027b226c9</cfClassId>
<cfClassSchemeId>40e90e2f-446d-460a-98e5-5dce57550c48</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
</cfResPubl_Class>
<cfPers_ResPubl>
<cfPersId>ibn-person-94405</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfPers_ResPubl>
<cfPersId>ibn-person-94406</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
</cfPers_ResPubl>
<cfPers_ResPubl>
<cfPersId>ibn-person-66049</cfPersId>
<cfClassId>49815870-1cfe-11e1-8bc2-0800200c9a66</cfClassId>
<cfClassSchemeId>b7135ad0-1d00-11e1-8bc2-0800200c9a66</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
</cfPers_ResPubl>
</cfResPubl>
<cfPers>
<cfPersId>ibn-Pers-94405</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-94405-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
<cfFamilyNames>Jolaoso</cfFamilyNames>
<cfFirstNames>Lateef Olakunle</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfPers>
<cfPersId>ibn-Pers-94406</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-94406-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
<cfFamilyNames>Ogbuisi</cfFamilyNames>
<cfFirstNames>Ferdinard Udochukwu</cfFirstNames>
</cfPersName_Pers>
</cfPers>
<cfPers>
<cfPersId>ibn-Pers-66049</cfPersId>
<cfPersName_Pers>
<cfPersNameId>ibn-PersName-66049-3</cfPersNameId>
<cfClassId>55f90543-d631-42eb-8d47-d8d9266cbb26</cfClassId>
<cfClassSchemeId>7375609d-cfa6-45ce-a803-75de69abe21f</cfClassSchemeId>
<cfStartDate>2021-12-03T24:00:00</cfStartDate>
<cfFamilyNames>Mewomo</cfFamilyNames>
<cfFirstNames>Oluwatosin Temitope</cfFirstNames>
</cfPersName_Pers>
</cfPers>
</CERIF>