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.
Keywords: $$-invex sets, strongly $$-invex sets, strongly $$-preinvex functions, nonlinear programming problem (NLPP)
@article{RO_2022__56_3_1397_0,
author = {Iqbal, Akhlad and Hussain, Askar},
title = {Nonlinear programming problem for strongly {\protect\emph{E}-invex} sets and strongly {\protect\emph{E}-preinvex} functions},
journal = {RAIRO. Operations Research},
pages = {1397--1410},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {3},
doi = {10.1051/ro/2022064},
mrnumber = {4437996},
zbl = {1508.90058},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022064/}
}
TY - JOUR AU - Iqbal, Akhlad AU - Hussain, Askar TI - Nonlinear programming problem for strongly E-invex sets and strongly E-preinvex functions JO - RAIRO. Operations Research PY - 2022 SP - 1397 EP - 1410 VL - 56 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022064/ DO - 10.1051/ro/2022064 LA - en ID - RO_2022__56_3_1397_0 ER -
%0 Journal Article %A Iqbal, Akhlad %A Hussain, Askar %T Nonlinear programming problem for strongly E-invex sets and strongly E-preinvex functions %J RAIRO. Operations Research %D 2022 %P 1397-1410 %V 56 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022064/ %R 10.1051/ro/2022064 %G en %F RO_2022__56_3_1397_0
Iqbal, Akhlad; Hussain, Askar. Nonlinear programming problem for strongly E-invex sets and strongly E-preinvex functions. RAIRO. Operations Research, Tome 56 (2022) no. 3, pp. 1397-1410. doi: 10.1051/ro/2022064
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