# On the Globalization of ASPIN Employing Trust-Region Control Strategies -- Convergence Analysis and Numerical Examples

arXiv: https://arxiv.org/abs/2104.05672 · HTML: https://mlsanity.com/paper/2104.05672/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2021.

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

- [A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks](https://mlsanity.com/paper/2305.14477/) (2023)
- [Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization](https://mlsanity.com/paper/2507.11513/) (2025)
- [Parallel Trust-Region Approaches in Neural Network Training: Beyond Traditional Methods](https://mlsanity.com/paper/2312.13677/) (2023)

## Abstract (arXiv)

The parallel solution of large scale non-linear programming problems, which arise for example from the discretization of non-linear partial differential equations, is a highly demanding task. Here, a novel solution strategy is presented, which is inherently parallel and globally convergent. Each global non-linear iteration step consists of asynchronous solutions of local non-linear programming problems followed by a global recombination step. The recombination step, which is the solution of a quadratic programming problem, is designed in a way such that it ensures global convergence. As it turns out, the new strategy can be considered as a globalized additively preconditioned inexact Newton (ASPIN) method. However, in our approach the influence of ASPIN's non-linear preconditioner on the gradient is controlled in order to ensure a sufficient decrease condition. Two different control strategies are described and analyzed. Convergence to first-order critical points of our non-linear solution strategy is shown under standard trust-region assumptions. The strategy is investigated along difficult minimization problems arising from non-linear elasticity in 3D solved on a massively parallel computer with several thousand cores.