Geodesic
Variational inequality problem over the solution set of split monotone variational inclusion problem with application to bilevel programming problem
Filomat, Tome 37 (2023) no. 24, p. 8361

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DOI

The purpose of this paper is to study variational inequality problem over the solution set of multiple-set split monotone variational inclusion problem. We propose an iterative algorithm with inertial method for finding an approximate solution of this problem in real Hilbert spaces. Strong convergence of the sequence of iterates generated from the proposed method is obtained under some mild assumptions. The iterative scheme does not require prior knowledge of operator norm. Also we present some applications of our main result to solve the bilevel programming problem, the bilevel monotone variational inequalities, the split minimization problem, the multiple-set split feasibility problem and the multiple set split variational inequality problem.
DOI : 10.2298/FIL2324361E
Classification : 47H05, 47H09, 49J53, 90C25
Keywords: Split monotone variational inclusion problem, bilevel programming problem, inertial algorithm 
M Eslamian. Variational inequality problem over the solution set of split monotone variational inclusion problem with application to bilevel programming problem. Filomat, Tome 37 (2023) no. 24, p. 8361 . doi: 10.2298/FIL2324361E
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     title = {Variational inequality problem over the solution set of split monotone variational inclusion problem with application to bilevel programming problem},
     journal = {Filomat},
     pages = {8361 },
     year = {2023},
     volume = {37},
     number = {24},
     doi = {10.2298/FIL2324361E},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2324361E/}
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