Projection Methods for Exponentially Regularized Nonconvex Variational Inequalities

Siyu Zhang; Sisheng Yao

doi:10.26689/ssr.v7i11.12971

Siyu Zhang School of Mathematics, Kunming University, Kunming 650214, Yunnan, China
Sisheng Yao School of Mathematics, Kunming University, Kunming 650214, Yunnan, China

DOI: https://doi.org/10.26689/ssr.v7i11.12971

Keywords: Nonconvex variational inequality, Uniformly r-prox-regular fixed point problems, Self-adaptive finite p-step projection algorithm

Abstract

This paper proposes a new exponentially regularized nonconvex variational inequality. The paper shows that the inequalities are equivalent to fixed point problems through the use of the projection properties. The paper develops a new self-adaptive projection iterative algorithm that not only dynamically adjusts the step size but also optimizes the projection direction, thereby improving the stability and convergence of the algorithm.

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