high-order proximal point algorithm for the monotone variational inequality problem and its application

2023/08/15 by Jingyu Gao, Gao, Jingyu, Xiurui Geng +1
Computer Science · Engineering · Mathematics · #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.2308.07689

Abstract

The proximal point algorithm (PPA) has been developed to solve the monotone variational inequality problem. It provides a theoretical foundation for some methods, such as the augmented Lagrangian method (ALM) and the alternating direction method of multipliers (ADMM). This paper generalizes the PPA to the pth-order (p≥ 1) and proves its convergence rate O (1/k^p/2) . Additionally, the pth-order ALM is proposed based on the pth-order PPA. Some numerical experiments are presented to demonstrate the performance of the pth-order ALM.

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