Nonlinear programming problem for strongly E-invex sets and strongly E-preinvex functions

Abstract

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.