Método extragradiente subgradiente com a técnica da proporção áurea para resolver problemas de equilíbrio em espaços de Hilbert

Abstract

In this thesis, we propose an accelerated and explicitly implementable subgradient extragradient method, based on the golden ratio technique, to solve pseudomonotone equilibrium problems in real Hilbert spaces. The algorithm assumes that the associated bifunction satisfies a Lipschitz-type condition, while incorporating a self-adaptive stepsize update rule that dispenses with prior knowledge of the Lipschitz-type constants, thus enhancing its practical applicability. Strong convergence of the generated sequence is ensured through the viscosity approximation technique. Moreover, under the additional assumption of strong pseudomonotonicity, we establish an R-linear convergence rate. To further improve performance, we introduce a second inertial step, whose effectiveness is validated by comparative numerical experiments. The results indicate that the proposed approach is theoretically consistent and computationally efficient.