# Convex optimization based on global lower second-order models

arXiv: https://arxiv.org/abs/2006.08518 · HTML: https://mlsanity.com/paper/2006.08518/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Second-order optimization with lazy Hessians](https://mlsanity.com/paper/2212.00781/) (2022)
- [ISAAC Newton: Input-based Approximate Curvature for Newton's Method](https://mlsanity.com/paper/2305.00604/) (2023)
- [Improving Stochastic Cubic Newton with Momentum](https://mlsanity.com/paper/2410.19644/) (2024)

## Abstract (arXiv)

In this paper, we present new second-order algorithms for composite convex optimization, called Contracting-domain Newton methods. These algorithms are affine-invariant and based on global second-order lower approximation for the smooth component of the objective. Our approach has an interpretation both as a second-order generalization of the conditional gradient method, or as a variant of trust-region scheme. Under the assumption, that the problem domain is bounded, we prove O(1/k2) global rate of convergence in functional residual, where k is the iteration counter, minimizing convex functions with Lipschitz continuous Hessian. This significantly improves the previously known bound O(1/k) for this type of algorithms. Additionally, we propose a stochastic extension of our method, and present computational results for solving empirical risk minimization problem.