Fe-convex Function and Fractional Semi-infinite Programming

A new class of generalized convex function called F_ε-convex and related nonconvex functions is defined, which generalize some of the present convex functions. By utilizing the new concepts, a class of fractional semi-infinite programming is studied; some interesting sufficient ε-optimality conditions are obtained. These results obtained not only extend some of the present researches, but also can be apply to the questions occur in resource allocation, stock cutting problem in paper industry, agricultural planning and portfolio selection etc. Theoretically, they are helpful to studying fractional semi-infinite programming.