On solutions and duality of nonlinear nonsmooth fractional programs

Dinkelbach's global optimization approach for finding the global maximum of the fractional programming problem is discussed. Based on this idea, we give several characterizations of the solution set of a convex-concave fractional programs. Nondifferentiability of the functions involved in the problem definition is assumed. The subgradients attaining the minimum principle are explicitly characterized, and this characterization is shown to be independent of any solution. Also a general dual is formulated and duality results are proved using concepts of dual space.