Issue |
RAIRO-Oper. Res.
Volume 56, Number 3, May-June 2022
|
|
---|---|---|
Page(s) | 1397 - 1410 | |
DOI | https://doi.org/10.1051/ro/2022064 | |
Published online | 13 June 2022 |
Nonlinear programming problem for strongly E-invex sets and strongly E-preinvex functions
Aligarh Muslim University, Aligarh 202002, India
* Corresponding author: askarhussain59@gmail.com
Received:
24
March
2021
Accepted:
4
May
2022
The concepts of strongly E-invex sets, strongly E-invex, strongly E-preinvex, and strongly pseudo E-preinvex functions are introduced in this paper. We have included several non-trivial examples to support our definitions. The family of strongly E-invex sets has been shown to form a vector space over R, and other interesting properties have been addressed. The epigraph of strongly E-preinvex function has been derived, as well as the relationship between the strongly E-preinvex function and the strongly pseudo E-preinvex function has been established. To show an important relationship between strongly E-invex and strongly E-preinvex functions, a new Condition A has been introduced. A nonlinear programming problem for strongly E-preinvex functions is explored as an application. Under a few conditions, it has been proved that the local minimum point is the global minimum for a nonlinear programming problem.
Mathematics Subject Classification: 26B25 / 26D07 / 90C25
Key words: E-invex sets / strongly E-invex sets / strongly E-preinvex functions / nonlinear programming problem (NLPP)
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.