Primal Acceleration of Newton's Method
Quick summary
arXiv:2608.21359v1 Announce Type: cross Abstract: We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian. The algorithm uses only primal variables and performs just one linear solve per iteration. With a simple predetermined choice of parameters, it achieves the global convergence rate of $O(1/k^3)$ in terms of the functional residual. To the best of our knowledge, this is the first second-order method for this problem class attaining this rate while relying solely on one linear system solve per iteration (without solving auxiliary n
Key takeaways
- arXiv:2608.21359v1 Announce Type: cross Abstract: We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian.
- The algorithm uses only primal variables and performs just one linear solve per iteration.
- With a simple predetermined choice of parameters, it achieves the global convergence rate of $O(1/k^3)$ in terms of the functional residual.
Why it matters
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