Volume 56, Number 3, May-June 2022
|1397 - 1410
|13 June 2022
Nonlinear programming problem for strongly E-invex sets and strongly E-preinvex functions
Aligarh Muslim University, Aligarh 202002, India
* Corresponding author: firstname.lastname@example.org
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.
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