2017/11/02 by Qiao‐Li Dong, Aviv Gibali, Dong, Qiao-Li +5
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1711.01937
openalex publication_date 2017/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning that an inexact version of the methods can also be considered. Moreover, once an algorithm is proved to be bounded perturbation resilience, superiorizion can be used, and this allows flexibility in choosing the bounded perturbations in order to obtain a superior solution, as well explained in the paper. We also discuss some inertial extragradient methods. Under mild and standard assumptions of monotonicity and Lipschitz continuity of the VI's associated mapping, convergence of the perturbed extragradient and subgradient extragradient methods is proved. In addition we show that the perturbed algorithms converges at the rate of O(1/t). Numerical illustrations are given to demonstrate the performances of the algorithms.