Linesearch methods for bilevel split pseudomonotone variational inequality problems

被引：21

作者：

Tran Viet Anh ^{[1
]}

机构：

[1] Posts & Telecommun Inst Technol, Dept Sci Fundamentals, Hanoi, Vietnam

来源：

NUMERICAL ALGORITHMS | 2019年 / 81卷 / 03期

关键词：

Bilevel split variational inequality problem; Linesearch methods; Pseudomonotone mapping; Strong convergence; ALGORITHMS;

D O I：

10.1007/s11075-018-0583-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose Linesearch methods for solving a bilevel split variational inequality problem (BSVIP) involving a strongly monotone mapping in the upper-level problem and pseudomonotone mappings in the lower-level one. A strongly convergent algorithm for such a BSVIP is proposed and analyzed.

引用

页码：1067 / 1087

页数：21

共 29 条

[1] Hybrid proximal point and extragradient algorithms for solving equilibrium problems
Anh P.N.
Hien N.D.
[J]. Acta Mathematica Vietnamica, 2014, 39 (3) : 405 - 423
[2] [Anonymous], 2001, INHERENTLY PARALLEL, DOI DOI 10.1016/S1570-579X(01)80028-8
[3] Algorithms for a class of bilevel programs involving pseudomonotone variational inequalities
Dinh B.V.
Muu L.D.
[J]. Acta Mathematica Vietnamica, 2013, 38 (4) : 529 - 540
[4] Relaxed extragradient methods for finding minimum-norm solutions of the split feasibility problem
Ceng, L. -C.
Ansari, Q. H.
Yao, J. -C.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) : 2116 - 2125
[5] The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space
Censor, Y.
Gibali, A.
Reich, S.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 148 (02) : 318 - 335
[6] The multiple-sets split feasibility problem and its applications for inverse problems
Censor, Y
Elfving, T
Kopf, N
Bortfeld, T
[J]. INVERSE PROBLEMS, 2005, 21 (06) : 2071 - 2084
[7] Algorithms for the Split Variational Inequality Problem
Censor, Yair
Gibali, Aviv
Reich, Simeon
[J]. NUMERICAL ALGORITHMS, 2012, 59 (02) : 301 - 323
[8] Censor Y, 2008, CRM SER, V7, P65
[9] A unified approach for inversion problems in intensity-modulated radiation therapy
Censor, Yair
Bortfeld, Thomas
Martin, Benjamin
Trofimov, Alexei
[J]. PHYSICS IN MEDICINE AND BIOLOGY, 2006, 51 (10) : 2353 - 2365
[10] Combettes PL, 2005, J NONLINEAR CONVEX A, V6, P117

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