A globally convergent method for nonlinear least-squares problems based on the Gauss-Newton model with spectral correction

Author(s)

Goncalves, Douglas S. ^[1] ; Santos, Sandra A. ^[2]

Affiliation

^[1] Univ Fed Santa Catarina, CCFM, Dept Math, BR-88040900 Florianopolis, SC - Brazil

^[2] Univ Estadual Campinas, IMECC, Dept Appl Math, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: BULLETIN OF COMPUTATIONAL APPLIED MATHEMATICS; v. 4, n. 2, p. 7-26, JUL-DEC 2016.
• Web of Science Citations: 1

Abstract

This work addresses a spectral correction for the Gauss-Newton model in the solution of nonlinear least-squares problems within a globally convergent algorithmic framework. The nonmonotone line search of Zhang and Hager is the chosen globalization tool. We show that the search directions obtained from the corrected Gauss-Newton model satisfy the conditions that ensure the global convergence under such a line search scheme. A numerical study assesses the impact of using the spectral correction for solving two sets of test problems from the literature. (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: 13/05475-7 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants