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math.OC2026
Generalized Quadratic Gradient: A New Direction in Optimization via the Fusion of Positive-Definite Curvature Matrices and Gradients into A Unified Framework
John Chiang
Quadratic Gradient (QG) is a Newton-type optimization framework that bridges first-order gradient descent and second-order optimization by incorporating curvature information into…
math.OC2026
Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization
John Chiang
In this paper, we introduce the Quasi-Quadratic Gradient (QQG), a novel search direction designed to accelerate the BFGS method within the quasi-Newton framework. By defining the Q…
math.OC2022
Simplified Quadratic Gradient: A Unified Framework Bridging Gradient Descent and Newton-Type Methods by Synthesizing Hessians and Gradients
John Chiang
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous…