An inertial Popov's method for solving pseudomonotone variational inequalities
In this paper, the authors present a new method to solve a variational inequality problem in Hilbert spaces. The method is modified from the traditional Popov's extragradient method using an inertial parameter. One of the major advantages of the proposed method is that only one value of the inequality mapping and one projection onto the admissible set per one iteration is computed. Furthermore, the requirement of prior knowledge of the Lipschitz constants of the variational inequality mapping is also relaxed. The goal is to accelerate the traditional Popov's algorithm. The authors present results on weak convergence of the proposed algorithm under pseudomonotonicity and Lipschitz continuity of the associated mapping. A section on numerical experiments validate the theoretical results. The theoretical results in the papaer are well presented and easy to follow. The proposed algorithm is certainly new in context of solving variational inequality problems. However, a couple of drawbacks of the paper are: first, the introduction primarily consists of standard definitions and notations rather than focusing on the major drawbacks of existing methods and highlighting the novelty of the proposed algorithm. For e.g., Popov's method, which is the basis of this work, and its motivation and significance is not described clearly. Second, the authors state in the abstract that their theoretical results generalize some well-known results in literature. It is not clear from the introduction and the body of the paper which results are being generalized. These two drawbacks lessen the impact of this important work.
scientific article; zbMATH DE number 7343979
scientific article