利用对单调性求解两个非单调算子之和问题的分裂算法

中文摘要 AI 辅助

本文关注在实希尔伯特空间中求解一个单值算子与一个集值算子之和的零点问题，且这两个算子均不假设为单调。在对单调性的框架下，我们提出了一种广义的前向-后向算法和一种广义的Tseng算法，这些算法基于与辅助线性算子相关的变换和扭曲预解式。我们在涉及对强单调性、对余强制性以及对Lipschitz连续性的适当假设下，建立了所提算法的弱收敛、强收敛和线性收敛。最后，通过数值实验验证了理论结果并展示了所提算法的有效性。

英文摘要

This paper is concerned with solving the problem of finding a zero of the sum of a single-valued operator and a set-valued operator, neither of which is assumed to be monotone, in a real Hilbert space. Under the framework of pair monotonicity, we propose a generalized forward--backward algorithm and a generalized Tseng algorithm based on transformed and warped resolvents associated with an auxiliary linear operator. We establish weak, strong and linear convergence of the proposed algorithms under suitable assumptions involving pair strong monotonicity, pair cocoercivity, and pair Lipschitz continuity. Finally, numerical experiments are presented to validate the theoretical results and demonstrate the effectiveness of the proposed algorithms.

发表机构

• Ton Duc Thang University（胡志明市镏德胜大学）
• Sidi Mohammed Ben Abdellah University, National School of Applied Sciences（西迪穆罕默德·本阿卜达拉大学国立应用科学学院）
• University of Limoges（利摩日大学）

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