Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization

TL;DR

The paper presents MASTR, a multilevel trust-region method with active-set strategy for efficiently solving large-scale non-convex bound-constrained minimization problems, especially from PDE discretizations.

Contribution

It introduces MASTR, a novel recursive multilevel trust-region method with an active-set approach that preserves variable bounds across levels for faster convergence.

Findings

Demonstrates fast convergence in numerical examples.

Effective preservation of variable bounds across multilevel hierarchy.

Suitable for large-scale PDE discretization problems.

Abstract

We introduce a novel variant of the recursive multilevel trust-region (RMTR) method, called MASTR. The method is designed for solving non-convex bound-constrained minimization problems, which arise from the finite element discretization of partial differential equations. MASTR utilizes an active-set strategy based on the truncated basis approach in order to preserve the variable bounds defined on the finest level by the coarser levels. Usage of this approach allows for fast convergence of the MASTR method, especially once the exact active-set is detected. The efficiency of the method is demonstrated by means of numerical examples.