On the Globalization of ASPIN Employing Trust-Region Control Strategies -- Convergence Analysis and Numerical Examples
Christian Gross, Rolf Krause

TL;DR
This paper introduces a novel, globally convergent, parallel solution strategy for large-scale non-linear programming problems, combining local asynchronous solutions with a global recombination step, and analyzes its convergence and numerical performance.
Contribution
It presents a new globally convergent parallel method based on ASPIN with controlled non-linear preconditioning and trust-region strategies.
Findings
Ensures global convergence for large-scale non-linear problems.
Demonstrates effectiveness on 3D non-linear elasticity problems.
Achieves parallel efficiency on massively parallel computers.
Abstract
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…
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Advanced Numerical Methods in Computational Mathematics
