Necessary optimality conditions of KKT type for interval programming problems

Authors

  • Valeriano Antunes de Oliveira
  • Fabiola Roxana Villanueva
  • Tiago Mendonça da Costa

DOI:

https://doi.org/10.5540/03.2021.008.01.0452

Keywords:

Interval Optimization Problems, Necessary Optimality Conditions, KKT Conditions.

Abstract

This work is concerned with mathematical programming problems with inequality constraints in which the objective function is interval-valued. Necessary optimality conditions of  Karush-Kuhn-Tucker type are derived through a geometric approach and the use of the generalized  Hukuhara differentiability concept.

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Author Biographies

Valeriano Antunes de Oliveira

Universidade Estadual Paulista (Unesp), Instituto de Biociências, Letras e Ciências Exatas, Departamento de Matemática, Câmpus de São José do Rio Preto, SP

Fabiola Roxana Villanueva

Universidade Estadual Paulista (Unesp), Instituto de Biociências, Letras e Ciências Exatas, Departamento de Matemática, Câmpus de São José do Rio Preto, SP

Tiago Mendonça da Costa

Universidade Estadual Paulista (Unesp), Instituto de Biociências, Letras e Ciências Exatas, Departamento de Matemática, Câmpus de São José do Rio Preto, SP

References

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Osuna-Gómez, R., Chalco-Cano, Y., Hernández-Jiménez, B. and Ruiz-Garzón, G. Optimality conditions for generalized differentiable interval-valued functions, Inform. Sciences, 321:136- 146, 2015. DOI: 10.1016/j.ins.2015.05.039.

Osuna-Gómez, R., Hernández-Jiménez, B., Chalco-Cano, Y. and Ruiz-Garzón, G. New efficiency conditions for multiobjective interval-valued programming problems, Inform. Sciences, 420:235-248, 2017.

Pal, B. B., Kumar, M. and Sen, S. A priority-based goal programming method for solving academic personnel planning problems with interval-valued resource goals in university man- agement system, Int. J. Appl. Manag. Sei., 4(3):284-312, 2012.

Stefanini, L. and Arana-Jiménez, M. Karush-Kuhn-Tucker conditions for interval and fuzzy optimization in several variables under total and directional generalized differentiability, Fuzzy Set. Syst., 362:1-34, 2019. DOI: 10.1016/j.fss.2018.04.009. 6

Stefanini, L. and Bede, B. Generalized Hukuhara differentiability of interval-valued func­ tions and interval differential equations, Nonlinear Anal.-Theor., 71 (3): 1311-1328, 2009. DOI: 10.1016/j.na.2008.12.005.

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Published

2021-12-20

Issue

Section

Trabalhos Completos