Sufficiency And Duality For Generalized Convex Infinite Fractional Programming

Optimality and duality conditions for fractional semi-infinite program-ming have particularly grown and become one of the most interesting topics in optimisation. The convexity concept plays an important factor in these conditions. Many authors have extended this concept and different kinds of functions. For the important role in optimization, it has extended in different ways. Many authors have written many papers, which directly or indirectly involved the optimality sufficient conditions and duality results in semi-infinite programming.We consider a continuously differentiable infinite fractional programming problem which invloves uncountably many inequality constraints. Based on the research results already obtained for semi-infinite fractional programming which has counterable number of inequality constraints, using the parametric approach that associates the original programming with an equivalent param-eter one, some new results concerning(1) sufficient optimality conditions;(2) weak duality and strong duality are obtained for the infinite fractional programming problem involving the class of generalized (F,α,ρ,θ)-d-V-univex functions.