ON HIGH-ORDER MODEL REGULARIZATION FOR CONSTRAINED OPTIMIZATION

Author(s)

Martinez, Jose Mario

• Document type: Journal article
• Source: SIAM JOURNAL ON OPTIMIZATION; v. 27, n. 4, p. 2447-2458, 2017.
• Web of Science Citations: 5

Abstract

In two recent papers regularization methods based on Taylor polynomial models for minimization were proposed that only rely on Holder conditions on the higher-order employedderivatives. 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. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 10/10133-0 - Cutting, packing, lot-sizing and scheduling problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
• Grantee: Carlos Eduardo Ferreira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/05475-7 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants