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A second-order dynamical system for equilibrium problems
A second-order dynamical system for equilibrium problems
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Date
2022
Authors
Le Van Vinh
Van Nam Tran
Phan Tu Vuong
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Abstract
We consider a second-order dynamical system for solving equilibrium problems
in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of
strong global solution of the proposed dynamical system. We establish the exponential
convergence of trajectories under strong pseudo-monotonicity and Lipschitz-type
conditions.We then investigate a discrete version of the second-order dynamical system,
which leads to a fixed point-type algorithm with inertial effect and relaxation.
The linear convergence of this algorithm is established under suitable conditions
on parameters. Finally, some numerical experiments are reported confirming the
theoretical results.
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Keywords
"Dynamic programming · Equilibrium problem · Monotonicity · Lipschitz continuity · Exponential stability · Linear convergence"