Abstract
The concepts of stronglyE-invex sets, stronglyE-invex, stronglyE-preinvex, and strongly pseudoE-preinvex functions are introduced in this paper. We have included several non-trivial examples to support our definitions. The family of stronglyE-invex sets has been shown to form a vector space overR, and other interesting properties have been addressed. The epigraph of stronglyE-preinvex function has been derived, as well as the relationship between the stronglyE-preinvex function and the strongly pseudoE-preinvex function has been established. To show an important relationship between stronglyE-invex and stronglyE-preinvex functions, a new Condition A has been introduced. A nonlinear programming problem for stronglyE-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.
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