Generalized Quadratic Gradient: A New Direction in Optimization via the Fusion of Positive-Definite Curvature Matrices and Gradients into A Unified Framework
Quadratic Gradient (QG) is a Newton-type optimization framework that bridges first-order gradient descent and second-order optimization by incorporating curvature information into gradient updates. Simplified Quadratic Gradient (SQG) reduces the complexity of QG construction while preserving its optimization capability, whereas Quasi-Quadratic Gradient (QQG) extends the quadratic gradient principle to quasi-Newton methods such as BFGS. In this paper, we propose **Generalized Quadratic Gradient (GQG)**, a unified framework that extends the quadratic gradient principle to a broader class of Newton-type optimization algorithms. By abstracting the common structure of existing quadratic gradie...
| Authors | John Chiang |
|---|---|
| Primary category | math.OC |
| Published | 3 August 2026 |
| Last updated at source | 3 August 2026 |
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