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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points

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Author(s):
Birgin, E. G. [1] ; Haeser, G. [2, 3] ; Ramos, A. [4]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Inst Math & Stat, Dept Comp Sci, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Sao Paulo, Inst Math & Stat, Dept Appl Math, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
[3] Stanford Univ, Dept Management Sci & Engn, Stanford, CA 94305 - USA
[4] Univ Fed Parana, Dept Math, Curitiba, PR - Brazil
Total Affiliations: 4
Document type: Journal article
Source: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 69, n. 1, p. 51-75, JAN 2018.
Web of Science Citations: 10
Abstract

Augmented Lagrangian methods with convergence to second-order stationary points in which any constraint can be penalized or carried out to the subproblems are considered in this work. The resolution of each subproblem can be done by any numerical algorithm able to return approximate second-order stationary points. The developed global convergence theory is stronger than the ones known for current algorithms with convergence to second-order points in the sense that, besides the flexibility introduced by the general lower-level approach, it includes a loose requirement for the resolution of subproblems. The proposed approach relies on a weak constraint qualification, that allows Lagrange multipliers to be unbounded at the solution. It is also shown that second-order resolution of subproblems increases the chances of finding a feasible point, in the sense that limit points are second-order stationary for the problem of minimizing the squared infeasibility. The applicability of the proposed method is illustrated in numerical examples with ball-constrained subproblems. (AU)

FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
Grantee:Carlos Eduardo Ferreira
Support type: Research Projects - Thematic Grants
FAPESP's process: 13/05475-7 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support type: Research Projects - Thematic Grants
FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:José Alberto Cuminato
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
Grantee:Reinaldo Morabito Neto
Support type: Research Projects - Thematic Grants
FAPESP's process: 16/02092-8 - On the second-order information in nonlinear optimization
Grantee:Gabriel Haeser
Support type: Scholarships abroad - Research