发表机构
National Center for Applied Mathematics in Chongqing, Chongqing Normal University（重庆应用数学中心，重庆师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于双曲主导化的预处理三项共轭梯度框架，用于非凸有限极小极大优化，通过解析对称正定度量同时实现曲率吸收、预处理和线搜索，保证充分下降、全局收敛并收敛到 Clarke 稳定点。
AI 中文摘要
本文针对非凸有限极小极大优化问题，提出了一种基于双曲主导化的预处理三项非线性共轭梯度框架。从双曲平滑模型的全局二次主导化出发，推导出一个解析的对称正定度量，该度量同时用作曲率吸收器、预处理器和线搜索能量度量。在位移 s_{k-1} 固定且曲率响应 b_k 可变的情况下，引入了一种增强的三项方向，并配以自适应参数 μ_k^\star，该参数在保持基线最坏情况度量能量常数的要求下取最大值。由此产生的框架具有 Dai-Liao 型共轭关系、增强的充分下降性、平滑参数一致的 Armijo 下界、固定平滑下的全局一阶收敛性和复杂度，以及在延拓下收敛到 Clarke 稳定点。
英文摘要
This paper develops a hyperbolic-majorization preconditioned three-term nonlinear conjugate-gradient framework for nonconvex finite minimax optimization. An analytic symmetric positive definite metric is derived from a global quadratic majorization of the hyperbolic smoothing model and is used simultaneously as a curvature absorber, a preconditioner, and the line-search energy metric. With the displacement \(s_{k-1}\) fixed and a variable curvature response \(b_k\), an enhanced three-term direction is introduced together with an adaptive parameter \(μ_k^\star\) that is maximal under the requirement that the baseline worst-case metric-energy constant be preserved. The resulting framework yields a Dai--Liao-type conjugacy relation, enhanced sufficient descent, a smoothing-parameter-uniform Armijo lower bound, fixed-smoothing global first-order convergence and complexity, and Clarke-stationary accumulation points under continuation.
