Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

A note on optimality conditions to interval optimization problems

Authors
Yurilev Chalco-Cano, Rafaela Osuna-Gómez, Beatriz Hernández-Jiménez, Heriberto Román-Flores
Corresponding Author
Yurilev Chalco-Cano
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.220How to use a DOI?
Keywords
Interval optimization, sufficient conditions, generalized convexity.
Abstract

In this article we examine to necessary and sufficient optimality conditions for interval optimization problems. We introduce a new concept of stationary point for an interval-valued function based on the gH-derivative. We show the importance the this concept from a practical and computational point of view. We introduce a new concept of invexity for gH-differentiable interval-valued function which generalizes previous concepts and we prove that it is a sufficient optimality condition. Finally, we show that the concepts of differentiability, convexity and invexity for interval-valued functions based on the differentiability, convexity and invexity of its endpoint functions are not adequate tools for interval optimization problems.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.220How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Yurilev Chalco-Cano
AU  - Rafaela Osuna-Gómez
AU  - Beatriz Hernández-Jiménez
AU  - Heriberto Román-Flores
PY  - 2015/06
DA  - 2015/06
TI  - A note on optimality conditions to interval optimization problems
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 1549
EP  - 1553
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.220
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.220
ID  - Chalco-Cano2015/06
ER  -