Improved inertial projection and contraction method for solving pseudomonotone variational inequality problems

Abstract

The objective of this article is to solve pseudomonotone variational inequality problems in a real Hilbert space. We introduce an inertial algorithm with a new self-adaptive step size rule, which is based on the projection and contraction method. Only one step projection is used to design the proposed algorithm, and the strong convergence of the iterative sequence is obtained under some appropriate conditions. The main advantage of the algorithm is that the proof of convergence of the algorithm is implemented without the prior knowledge of the Lipschitz constant of cost operator. Numerical experiments are also put forward to support the analysis of the theorem and provide comparisons with related algorithms.

Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature

“…Specially, since the sectional curvature of n is equal to 0, the parameter τ n is chosen as ∞ for n ≥ 0. This algorithm is different from the existing inertial methods for solving variational inequalities in n [24,28,34,40].…”

“…In the past few years, different iterative methods with inertial terms have been proposed for soling variational inequalities in Hilbert spaces [24,28,34,40]. By using inertial extrapolation techniques, the convergence speed of some iterative methods can be effectively accelerated.…”

New Convergence Theorems for Pseudomonotone Variational Inequality on Hadamard Manifolds

“…The main advantages of these extensions are that non-convex problems and constrained problems in spaces with linear structure and symmetry may be transformed into convex problems and unconstrained problems on Hadamard manifolds without linear structure, respectively. So, many nonlinear problems on symmetric Hadamard manifolds have been attracted and studied by some authors, see for example [19][20][21][22][23][24][25][26][27][28][29] and the reference therein.…”