A Note on Optimality Conditions to Interval Optimization Problems:. Chalco-Cano, Y., Osuna-Gómez, R., Hernández-Jiménez, B., & Román-Flores, H. In Gijón, Spain., 2015. 4 citations (Semantic Scholar/DOI) [2023-03-03]Paper doi abstract bibtex 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.
@inproceedings{chalco-cano_note_2015,
address = {Gijón, Spain.},
title = {A {Note} on {Optimality} {Conditions} to {Interval} {Optimization} {Problems}:},
shorttitle = {A {Note} on {Optimality} {Conditions} to {Interval} {Optimization} {Problems}},
url = {https://www.atlantis-press.com/article/23731},
doi = {10.2991/ifsa-eusflat-15.2015.220},
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.},
language = {en},
urldate = {2022-01-19},
author = {Chalco-Cano, Yurilev and Osuna-Gómez, Rafaela and Hernández-Jiménez, Beatriz and Román-Flores, Heriberto},
year = {2015},
note = {4 citations (Semantic Scholar/DOI) [2023-03-03]},
keywords = {/unread},
}
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