发表机构
College of Information Science and Technology, Jinan University; School of Mathematics, South China University of Technology（暨南大学信息科学技术学院; 华南理工大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对广义绝对值方程和线性互补问题这类可表述为互补集上最小二乘问题的模型，提出保障投影梯度框架，分析其收敛性质，通过数值实验展示该框架在测试中的高精度及相关计算权衡等实际表现。
AI 中文摘要
广义绝对值方程（GAVEs）和线性互补问题（LCPs）出现在许多均衡和优化模型中，且都可表述为互补集上的最小二乘问题。基于此共同表述，我们为这两类问题提出一种带有问题相关代数细化的保障投影梯度框架。我们分析其收敛性质，并在更强条件下建立唯一解的有限恢复。在GAVE和LCP基准上的数值实验说明了该框架的实际表现，包括在测试设置中的高最终精度及其与问题相关的计算权衡。
英文摘要
Both generalized absolute value equations (GAVEs) and linear complementarity problems (LCPs) can be formulated as least-squares problems over the complementarity set. Because this feasible set is nonconvex, projected stationarity does not in general imply zero residual. We develop a safeguarded projected-gradient framework with a linear-system refinement on a selected polyhedral face. We establish matrix conditions under which every projected stationary point is a global solution and derive corresponding global convergence results. Specifically, when refinement on a correct active face returns a solution, we give explicit iteration bounds for active-face identification and prove finite termination. Numerical experiments on GAVE and LCP benchmarks demonstrate the high accuracy of the proposed framework across the tested settings.
