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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA18-06915S" target="_blank" >GA18-06915S: Nové přístupy k agregačním operátorům v analýze a zpracování dat</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

INFORMATION SCIENCES

ISSN

0020-0255

e-ISSN

—

Svazek periodika

510

Číslo periodika v rámci svazku

FEB

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

317-340

Kód UT WoS článku

000494053000020

EID výsledku v databázi Scopus

2-s2.0-85072675046