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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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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Abstract 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.
AbstractList 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.
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(1k) 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.
Author Anh, P. N.
Hien, N. D.
Thang, T. V.
Thach, H. T. C.
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  surname: Thang
  fullname: Thang, T. V.
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  givenname: N. D.
  surname: Hien
  fullname: Hien, N. D.
  email: nguyenduchien@dtu.edu.vn
  organization: Duy Tan University
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  givenname: H. T. C.
  surname: Thach
  fullname: Thach, H. T. C.
  organization: University of Transport Technology
– sequence: 4
  givenname: P. N.
  surname: Anh
  fullname: Anh, P. N.
  organization: Posts and Telecommunications Institute of Technology
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Snippet In this work, we introduce an inertial proximal algorithm for solving multivalued variational inequality problems in a real Hilbert space. By using...
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SubjectTerms Adaptive algorithms
Convergence
Hilbert space
inertial technique
Lipschitz continuous
monotone
Multivalued variational inequality problems
Operators (mathematics)
proximal operator
self adaptive stepsize
Title Weak convergence of inertial proximal algorithms with self adaptive stepsize for solving multivalued variational inequalities
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