Optimality conditions and duality in fractional programming involving semilocally preinvex and related functions

In this paper, a nonlinear fractional programming problem is considered, where the functions involved are η-semidifferentiable. Necessary and sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using concepts of semilocally preinvex, semilocally quasi-preinvex and semilocally pseudo-preinvex functions. Our results generalize the results obtained by Lyall et al.