2016
DOI: 10.1016/j.amc.2016.06.007
|View full text |Cite
|
Sign up to set email alerts
|

The conjugate gradient method for split variational inclusion and constrained convex minimization problems

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
5

Citation Types

0
8
0

Year Published

2018
2018
2023
2023

Publication Types

Select...
6

Relationship

2
4

Authors

Journals

citations
Cited by 6 publications
(8 citation statements)
references
References 16 publications
0
8
0
Order By: Relevance
“…and such that y * � Tx * ∈ H 2 solves θ ∈ A 2 y * 􏼁 + M 2 y * 􏼁, (5) where θ is the zero vector in H 1 and H 2 , M 1 : H 1 ⟶ 2 H 1 and M 2 : H 2 ⟶ 2 H 2 are multivalued mappings on H 1 and H 2 , A 1 : H 1 ⟶ H 1 and A 2 : H 2 ⟶ H 2 are two given singlevalued mappings, and T: H 1 ⟶ H 2 is a bounded linear operator with adjoint T * of T. We note that if (4) and ( 5) are considered separately, we have that ( 4) is a variational inclusion problem with its solution set VI(H 1 , A 1 , M 1 ) and ( 5) is a variational inclusion problem with its solution set VI(H 1 , A 2 , M 2 ). We denoted the set of all solutions of (SMVI) by Ω � x * ∈ VI(H 1 , A 1 , M 1 ):…”
Section: Introductionmentioning
confidence: 99%
“…and such that y * � Tx * ∈ H 2 solves θ ∈ A 2 y * 􏼁 + M 2 y * 􏼁, (5) where θ is the zero vector in H 1 and H 2 , M 1 : H 1 ⟶ 2 H 1 and M 2 : H 2 ⟶ 2 H 2 are multivalued mappings on H 1 and H 2 , A 1 : H 1 ⟶ H 1 and A 2 : H 2 ⟶ H 2 are two given singlevalued mappings, and T: H 1 ⟶ H 2 is a bounded linear operator with adjoint T * of T. We note that if (4) and ( 5) are considered separately, we have that ( 4) is a variational inclusion problem with its solution set VI(H 1 , A 1 , M 1 ) and ( 5) is a variational inclusion problem with its solution set VI(H 1 , A 2 , M 2 ). We denoted the set of all solutions of (SMVI) by Ω � x * ∈ VI(H 1 , A 1 , M 1 ):…”
Section: Introductionmentioning
confidence: 99%
“…The SVIP has been applied to solving many real life problems, such as, modelling intensitymodulated radiation therapy treatment planning [7,8], and modelling of inverse problems arising from phase retrieval [4]. Recently, a lot of projection algorithms were proposed to solve the SVIP (1.1)-(1.2) in infinite-dimensional spaces; see, e.g., [2,5,6,11,12,13,23,25] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…which is applied to intensity-modulated radiation therapy [1][2][3][4][5][6][7][8][9][10][11], signal processing [12][13][14][15][16][17][18][19][20][21], and image reconstruction [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Censor et al [39] proposed the proximity function pðxÞ to measure the distance of a point to all sets…”
Section: Introductionmentioning
confidence: 99%