Newton-type multilevel optimization method

Chin Pang Ho, Michal Kocvara, Panos Parpas

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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 languageEnglish
Number of pages33
JournalOptimization Methods and Software
Early online date13 Dec 2019
DOIs
Publication statusE-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

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