On High-order Model Regularization for Constrained Optimization

Author:
  • JMJosé Mario Martínez
    José Mario Martínez
Publisher website
Google Scholar
Abstract
In two recent papers regularization methods based on Taylor polynomial models for minimization were proposed that only rely on Hölder conditions on the higher-order employed derivatives. Grapiglia and Nesterov considered cubic regularization with a sufficient descent condition that uses the current gradient and resembles the classical Armijo's criterion. Cartis, Gould, and Toint used Taylor models with arbitrary-order regularization and defined methods that tackle convex constraints employing the descent criterion that compares actual reduction with predicted reduction. The methods presented in this paper consider general (not necessarily Taylor) models of arbitrary order, employ a very mild descent criterion, and handle general, nonnecessarily convex, constraints. Complexity results are compatible with the ones presented in the papers mentioned above.
Funding Information
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (2010/10133-0)
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (2013/03447-6, 2013/05475-7, 2013/07375-0)
  • Conselho Nacional de Desenvolvimento Científico e Tecnológico

This publication has 25 references indexed in Scilit: