Analysis of a class of fractional programming problems

The paper proposes a solution strategy for fractional programming problems of the form maxxÅ∈Xg(x)/ø(u(x)), where the function ø satisfies certain convexity conditions. It is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem maxxÅ∈Xg(x)+λu(x), where λ is an exogeneous parameter. The proposed strategy combines fractional programming and c-programming techniques. A maximal mean-standard deviation ratio problem is solved to illustrate the strategy in action.