Stochastic Heavy-Ball Method for Constrained Stochastic Optimization Problems


In this paper, we consider a heavy-ball method for the constrained stochastic optimization problem by focusing to the situation that the constraint set is specified as the intersection of possibly finitely many constraint sets. A variant algorithm of the stochastic heavy-ball method is proposed which will be incrementally processed by both the stochastic heavy-ball method and random constraint projection simultaneously. They converge almost surely to a solution of the suggested method is exhibited. Finally, a numerical experiment is discussed.

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This study is supported by the Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0023/2555).

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Correspondence to Narin Petrot.

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Promsinchai, P., Farajzadeh, A. & Petrot, N. Stochastic Heavy-Ball Method for Constrained Stochastic Optimization Problems. Acta Math Vietnam 45, 501–514 (2020).

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  • Constrained stochastic optimization problem
  • Heavy-ball method
  • Random projection method
  • Converge almost surely

Mathematics Subject Classification (2010)

  • 90C15
  • 90C25
  • 90C06
  • 65K05