Weak and Error-Bound Linear Convergence of a Safeguarded Anderson-Accelerated Subgradient Extragradient Method

Abstract

We propose a safeguarded Anderson-accelerated subgradient extragradient method for variational inequalities in real Hilbert spaces. The method combines classical projection onto the feasible set with an explicit projection onto a supporting half space and finite memory Anderson correction. A self-adaptive step size with a summable additive recovery sequence is used without prior knowledge of the Lipschitz constant. Weak convergence is established under a solution-oriented condition that does not require monotonicity or pseudomonotonicity. Under a local projection-residual error bound, we obtain Q-linear convergence of the distance to the solution set and strong R-linear convergence of the iterates without assuming uniqueness. Numerical experiments on a dense nonlinear orthogonal transform variational inequality, and a dense nonlinear network consensus model illustrates the performance of the method.