Weak convergence of inertial proximal algorithms with self adaptive stepsize for solving multivalued variational inequalities

In this work, we introduce an inertial proximal algorithm for solving multivalued variational inequality problems in a real Hilbert space. By using self-adaptive and inertial techniques via proximal operators, we establish the weak convergence of the iteration sequences generated by these algorithms...

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Bibliographic Details
Published inOptimization Vol. 73; no. 4; pp. 995 - 1023
Main Authors Thang, T. V., Hien, N. D., Thach, H. T. C., Anh, P. N.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.04.2024
Taylor & Francis LLC
Subjects
Adaptive algorithms
Convergence
Hilbert space
inertial technique
Lipschitz continuous
monotone
Multivalued variational inequality problems
Operators (mathematics)
proximal operator
self adaptive stepsize
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Summary:In this work, we introduce an inertial proximal algorithm for solving multivalued variational inequality problems in a real Hilbert space. By using self-adaptive and inertial techniques via proximal operators, we establish the weak convergence of the iteration sequences generated by these algorithms when the multivalued cost mappings associated with the problems are monotone and Lipschitz continuous. Moreover, we present the nonasymptotic $ O(\frac {1}{k}) $ O ( 1 k ) convergence rate of the proposed algorithms. We also provide some numerical examples to illustrate the accuracy and efficiency of our algorithms by comparing with other recent algorithms in the literature.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2135966