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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 possible infeasibility and finite termination for global nonlinear programming

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Author(s):
Birgin, E. G. [1] ; Martinez, J. M. [2] ; Prudente, L. F. [2]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Dept Comp Sci, Inst Math & Stat, Sao Paulo - Brazil
[2] Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Global Optimization; v. 58, n. 2, p. 207-242, FEB 2014.
Web of Science Citations: 9
Abstract

In a recent paper, Birgin, Floudas and Martinez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the BB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given. (AU)

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: 06/53768-0 - Computational methods of optimization
Grantee:José Mário Martinez Perez
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 09/10241-0 - Theory and software in computational methods for optimization
Grantee:Ernesto Julián Goldberg Birgin
Support Opportunities: Regular Research Grants