A hybrid epigraph directions method for nonsmooth and nonconvex constrained optimization via generalized augmented Lagrangian duality and a genetic algorithm
type: Item
instance of: scholarly article
title: A hybrid epigraph directions method for nonsmooth and nonconvex constrained optimization via generalized augmented Lagrangian duality and a genetic algorithm
zbMATH Open document ID: 1427.90261
DOI: 10.1155/2018/8750740
author: Wilhelm P. Freire
author: Afonso C. C. Lemonge
author: T. Fonseca
author: H. Franco
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C56
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 7019664
describes a project that uses: Matlab
describes a project that uses: NSO
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8750740
OpenAlex ID: W2804781939
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Wikidata QID: Q129776623
description: scientific article; zbMATH DE number 7019664