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A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm
Joint Authors
Freire, Wilhelm P.
Lemonge, Afonso C. C.
Fonseca, Tales L.
Franco, Hernando J. R.
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-05-22
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
The Interior Epigraph Directions (IED) method for solving constrained nonsmooth and nonconvex optimization problem via Generalized Augmented Lagrangian Duality considers the dual problem induced by a Generalized Augmented Lagrangian Duality scheme and obtains the primal solution by generating a sequence of iterates in the interior of the epigraph of the dual function.
In this approach, the value of the dual function at some point in the dual space is given by minimizing the Lagrangian.
The first version of the IED method uses the Matlab routine fminsearch for this minimization.
The second version uses NFDNA, a tailored algorithm for unconstrained, nonsmooth and nonconvex problems.
However, the results obtained with fminsearch and NFDNA were not satisfactory.
The current version of the IED method, presented in this work, employs a Genetic Algorithm, which is free of any strategy to handle the constraints, a difficult task when a metaheuristic, such as GA, is applied alone to solve constrained optimization problems.
Two sets of constrained optimization problems from mathematics and mechanical engineering were solved and compared with literature.
It is shown that the proposed hybrid algorithm is able to solve problems where fminsearch and NFDNA fail.
American Psychological Association (APA)
Freire, Wilhelm P.& Lemonge, Afonso C. C.& Fonseca, Tales L.& Franco, Hernando J. R.. 2018. A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-21.
https://search.emarefa.net/detail/BIM-1209468
Modern Language Association (MLA)
Freire, Wilhelm P.…[et al.]. A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm. Mathematical Problems in Engineering No. 2018 (2018), pp.1-21.
https://search.emarefa.net/detail/BIM-1209468
American Medical Association (AMA)
Freire, Wilhelm P.& Lemonge, Afonso C. C.& Fonseca, Tales L.& Franco, Hernando J. R.. A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-21.
https://search.emarefa.net/detail/BIM-1209468
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209468