Abstract
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the optimization model, and as a result, they outperform single-level methods, especially for large-scale models. The impressive performance of multilevel optimization methods is an empirical observation, and no theoretical explanation has so far been proposed. In order to address this issue, we study the convergence properties of a multilevel method that is motivated by second-order methods. We take the first step toward establishing how the structure of an optimization problem is related to the convergence rate of multilevel algorithms.
Original language | English |
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Number of pages | 33 |
Journal | Optimization Methods and Software |
Early online date | 13 Dec 2019 |
DOIs | |
Publication status | E-pub ahead of print - 13 Dec 2019 |
Keywords
- Newton's method
- multigrid methods
- multilevel algorithms
- unconstrained optimization
ASJC Scopus subject areas
- Software
- Control and Optimization
- Applied Mathematics