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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

arXiv · AI, language, vision and robotics · article · Sep 11, 2026 · UTC

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

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