A Projection Anderson Acceleration Algorithm for Non-quasi-monotone Variational Inequalities with Hölder Continuous Terms
Abstract
This paper proposes a Projection Anderson Acceleration (PAA) algorithm for variational inequality (VI) problems, where the underlying function is expressed as a finite sum of Hölder continuous functions and satisfies the σ-star strongly monotone condition that includes the star strong monotonicity with σ= 1 as a special case. In the absence of quasi-monotonicity and Lipschitz continuity, we establish the evaluation complexity of the PAA algorithm for finding an approximate solution. Specifically, for the star strongly monotone VI problems, the PAA algorithm needs at most O (log (ε−1) ε2 (underlineα − 1)) evaluations of the function and projection for finding an ε-approximate solution, where underlineα ∈ (0, 1] is the smallest exponent of H{ö}lder continuity of the component functions. We illustrate our theoretical results by numerical examples of non-quasi-monotone complementarity problems and non-monotone semilinear elliptic equations with non-Lipschitz terms.
Related
- On Fixed-Time Stability of Continuous Dynamics for Non-Monotone Variational Inequalities
- Boundary Projection Acceleration for 2D One-cell Inversions in the Scattering Limit
- Acceleration of the BSS Algorithm
- Acceleration and its Limits in Gaussian Variational Inference
- A Projection Identity for Simplices Sharp Inequalities, Converse Results, and Affine Projections
BibTeX
@misc{chen2026projection,
title = {{A Projection Anderson Acceleration Algorithm for Non-quasi-monotone Variational Inequalities with Hölder Continuous Terms}},
author = {Xiaojun Chen and C. T. Kelley and Lei Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18370},
eprint = {2610.18370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18370},
}
RIS
TY - UNPB
TI - A Projection Anderson Acceleration Algorithm for Non-quasi-monotone Variational Inequalities with Hölder Continuous Terms
AU - Xiaojun Chen
AU - C. T. Kelley
AU - Lei Wang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18370
UR - https://arxiv.org/abs/2610.18370
AB - This paper proposes a Projection Anderson Acceleration (PAA) algorithm for variational inequality (VI) problems, where the underlying function is expressed as a finite sum of Hölder continuous functions and satisfies the σ-star strongly monotone condition that includes the star strong monotonicity with σ= 1 as a special case. In the absence of quasi-monotonicity and Lipschitz continuity, we establish the evaluation complexity of the PAA algorithm for finding an approximate solution. Specifically, for the star strongly monotone VI problems, the PAA algorithm needs at most O (log (ε^−1) ε^2 (underlineα − 1)) evaluations of the function and projection for finding an ε-approximate solution, where underlineα ∈ (0, 1] is the smallest exponent of H{ö}lder continuity of the component functions. We illustrate our theoretical results by numerical examples of non-quasi-monotone complementarity problems and non-monotone semilinear elliptic equations with non-Lipschitz terms.
ER -