Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

Author(s)

Birgin, E. G. ; Gardenghi, J. L. ; Martinez, J. M. ; Santos, S. A. ; Toint, Ph. L.

• Document type: Journal article
• Source: MATHEMATICAL PROGRAMMING; v. 163, n. 1-2, p. 359-368, MAY 2017.
• Web of Science Citations: 23

Abstract

The worst-case evaluation complexity for smooth (possibly nonconvex) unconstrained optimization is considered. It is shown that, if one is willing to use derivatives of the objective function up to order p (for p >= 1) and to assume Lipschitz continuity of the p-th derivative, then an epsilon-approximate first-order critical point can be computed in at most O(epsilon -((p+1)/p)) evaluations of the problem's objective function and its derivatives. This generalizes and subsumes results known for p = 1 and p = 2. (AU)

• 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: 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: 13/23494-9 - Large-scale linearly constrained minimization with convergence to second order stationary points
• Grantee: John Lenon Cardoso Gardenghi
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 13/05475-7 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants
• 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