Generalized Hukuhara Gateaux and Frechet derivatives of interval-valued functions and their application in optimization with interval-valued functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603766" target="_blank" >RIV/61989592:15310/20:73603766 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0020025519308746" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0020025519308746</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ins.2019.09.023" target="_blank" >10.1016/j.ins.2019.09.023</a>

Result language
angličtina
Original language name
Generalized Hukuhara Gateaux and Frechet derivatives of interval-valued functions and their application in optimization with interval-valued functions
Original language description
In this article, the notions of gH-directional derivative, gH-Gateaux derivative and gH-Frechet derivative for interval-valued functions are proposed. The existence of gH-Frechet derivative is shown to imply the existence of gH-Gateaux derivative and the existence of gH-Gateaux derivative is observed to indicate the presence of gH-directional derivative. For an interval valued gH-Lipschitz function, it is proved that the existence of gH-Gateaux derivative implies the existence of gH-Frechet derivative. It is observed that for an interval-valued convex function on a linear space, the gH-directional derivative exists at any point for every direction. Concepts of linear and monotonic interval-valued functions are studied in the sequel. Further, it is shown that the proposed derivatives are useful to check the convexity of an interval-valued function and to characterize efficient points of an optimization problem with interval-valued objective function. It is observed that at an efficient point of an interval-valued function, none of its gH-directional derivatives dominates zero and the gH-Gateaux derivative must contain zero. The entire study is supported by suitable illustrative examples.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA18-06915S" target="_blank" >GA18-06915S: New approaches to aggregation operators in analysis and processing of data</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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