| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Estadual Campinas, Dept Appl Math, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
[2] Univ Sao Paulo, Dept Appl Math, Rua Matao 1010 Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
[3] Univ Fed Parana, Dept Math, Curitiba 19-081, BR-81531980 Curitiba, PR - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | IMA JOURNAL OF NUMERICAL ANALYSIS; v. 37, n. 4, p. 1902-1929, OCT 2017. |
| Web of Science Citations: | 8 |
| Abstract | |
Sequential optimality conditions have recently played an important role on the analysis of the global convergence of optimization algorithms towards first-order stationary points, justifying their stopping criteria. In this article, we introduce a sequential optimality condition that takes into account second-order information and that allows us to improve the global convergence assumptions of several second-order algorithms, which is our main goal. We also present a companion constraint qualification that is less stringent than previous assumptions associated to the convergence of second-order methods, like the joint condition Mangasarian-Fromovitz and weak constant rank. Our condition is also weaker than the constant rank constraint qualification. This means that we can prove second-order global convergence of well-established algorithms even when the set of Lagrange multipliers is unbounded, which was a limitation of previous results based on Mangasarian-Fromovitz constraint qualification. We prove global convergence of well-known variations of the augmented Lagrangian and regularized sequential quadratic programming methods to second-order stationary points under this new weak constraint qualification. (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 |
| FAPESP's process: | 12/20339-0 - Penalty methods, optimality conditions, and applications |
| Grantee: | Paulo José da Silva e Silva |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 10/19720-5 - Optimality conditions and inexact restoration |
| Grantee: | Gabriel Haeser |
| Support Opportunities: | Research Grants - Young Investigators Grants |