A Dynamical System for Strongly Pseudo-monotone Equilibrium Problems
Phan Tu Vuong, Jean Jacques Strodiot
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.
Topics & Concepts
MathematicsLipschitz continuityProjected dynamical systemHilbert spaceMonotonic functionDynamical systems theoryTheory of computationMonotone polygonApplied mathematicsDynamical system (definition)Strongly monotoneConvergence (economics)Rate of convergenceTrajectoryLinear dynamical systemMathematical analysisRandom dynamical systemLinear systemComputer scienceGeometryQuantum mechanicsEconomic growthComputer networkAstronomyEconomicsPhysicsAlgorithmChannel (broadcasting)Optimization and Variational AnalysisAdvanced Optimization Algorithms ResearchContact Mechanics and Variational Inequalities