A Linear Fractional Max-Min Problem

This paper is concerned with a linear fractional problem of the form: max_X min_YF(X, Y) = (cX + dY + α)/(fX + gY + β), subject to

This problem represents a generalization of a problem considered in the literature in which F(X, Y) is assumed to be linear. A number of results for the linear case are extended; and, in particular, it is shown that this fractional max-min problem is equivalent to a quasi-convex programming problem whose optimal solution lies at a vertex of the feasible region. Using these results, we develop an algorithm for solving this problem. The paper concludes with a numerical example.