A Dynamical System for Strongly Pseudo-monotone Equilibrium Problems

Phan Tu Vuong () and Jean Jacques Strodiot ()
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Phan Tu Vuong: University of Southampton
Jean Jacques Strodiot: University of Namur

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 5, 767-784

Abstract: Abstract In this paper, we consider a dynamical system for solving equilibrium problems in the framework of Hilbert spaces. First, we prove that under strong pseudo-monotonicity and Lipschitz-type continuity assumptions, the dynamical system has a unique equilibrium solution, which is also globally exponentially stable. Then, we derive the linear rate of convergence of a discrete version of the proposed dynamical system to the unique solution of the problem. Global error bounds are also provided to estimate the distance between any trajectory and this unique solution. Some numerical experiments are reported to confirm the theoretical results.

Keywords: Equilibrium problem; Dynamical system; Strong pseudo-monotonicity; Global exponential stability; Error bound; 47J20; 49J40; 49M30 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-020-01669-y

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