Nonlinear programming problem for strongly E -invex sets and strongly E -preinvex functions - Iqbal, Akhlad; Hussain, Askar (R.A.I.R.O. Recherche opérationnelle, 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.