A note on optimality conditions to interval optimization problems
- https://doi.org/10.2991/ifsa-eusflat-15.2015.220How to use a DOI?
- Interval optimization, sufficient conditions, generalized convexity.
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.
- © 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 -