一类基于修正拟牛顿更新的最小二乘逼近谱共轭梯度算法族及其在修正鲁棒二分类模型中的应用
A family of spectral conjugate gradient algorithms derived by least-squares approximations based on a modified quasi--Newton update with application to a revised robust binary classification model
- Free University of Bozen–Bolzano（博尔扎诺自由大学）
- Semnan University（塞姆南大学）
- American University（美利坚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一类基于最小二乘逼近和修正拟牛顿更新的谱三项共轭梯度算法，保证充分下降与收敛性，并在CUTEr测试集及鲁棒二分类SVM应用中验证其优势。
AI中文摘要：
我们开发了经典Hestenes-Stiefel共轭梯度算法的谱三项修正版本，保留了其抗干扰特性，同时兼顾了充分下降性质。我们讨论了如何从我们的修正方案中提取修正割线方程，从而得到无记忆BFGS更新公式。然后，通过最小二乘框架将方向引导至给定的BFGS方向，获得我们方法的谱参数。利用我们的技术改进，我们概述了算法的一般框架，并讨论了其理论特性，包括无需凸性假设的下降性和收敛性。我们将算法与另外三种共轭梯度算法在CUTEr无约束优化测试模型集合上进行比较测试，使用Dolan-More度量比较输出结果。接下来，我们对结果进行简要评估，突出我们算法的实际优势。作为真实世界案例研究，我们引入了一种带有重缩放损失的约化二次曲面SVM用于鲁棒二分类，并将所提算法应用于评估其准确性和训练时间，与几种其他SVM进行比较。
英文摘要：
We develop a spectral three-term modification of the classic Hestenes--Stiefel conjugate gradient algorithm, preserving its anti-jamming characteristic and, simultaneously, taking care of the sufficient descent property. We discuss how a modified secant equation can be extracted from our modification scheme, yielding a memoryless BFGS updating formula. Then, the spectral parameter of our method is obtained by steering its direction toward the given BFGS direction within a least-squares context. Using our technical improvements, we outline the general framework of our algorithm and discuss its theoretical features, including the descent and convergence properties, without the convexity assumption. We put our algorithm to the test in comparison with the three other conjugate gradient algorithms on a set of CUTEr unconstrained optimization test models, comparing the outputs using the Dolan--More measure. Next, we provide a concise evaluation of the results, highlighting the practical advantages of our algorithm. As a real-world case study, we introduce a reduced quadratic surface SVM with the rescaled loss for robust binary classification and apply the proposed algorithm to assess its accuracy and training time against several other SVMs.
