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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.)

Bilevel optimization with a multiobjective problem in the lower level

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Author(s):
Andreani, Roberto [1] ; Ramirez, Viviana A. [2] ; Santos, Sandra A. [1] ; Secchin, Leonardo D. [3]
Total Authors: 4
Affiliation:
[1] Univ Estadual Campinas, Inst Math, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil
[2] Natl Univ Comahue, Acad Reg Ctr Bariloche, Quintral 1250, San Carlos De Bariloche, Rio Negro - Argentina
[3] Univ Fed Espirito Santo, Dept Appl Math, Rodovia BR 101, Km 60, BR-29932540 Sao Mateus, ES - Brazil
Total Affiliations: 3
Document type: Journal article
Source: NUMERICAL ALGORITHMS; v. 81, n. 3, p. 915-946, JUL 2019.
Web of Science Citations: 0
Abstract

Bilevel problems model instances with a hierarchical structure. Aiming at an efficient solution of a constrained multiobjective problem according with some pre-defined criterion, we reformulate this semivectorial bilevel optimization problem as a classic bilevel one. This reformulation intents to encompass all the objectives, so that the properly efficient solution set is recovered by means of a convenient weighted-sum scalarization approach. Inexact restoration strategies potentially take advantage of the structure of the problem under consideration, being employed as an alternative to the Karush-Kuhn-Tucker reformulation of the bilevel problem. Genuine multiobjective problems possess inequality constraints in their modeling, and these constraints generate theoretical and practical difficulties to our lower level problem. We handle these difficulties by means of a perturbation strategy, providing the convergence analysis, together with enlightening examples and illustrative numerical tests. (AU)

FAPESP's process: 13/05475-7 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support Opportunities: Research Projects - Thematic Grants
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