An Algorithm for a Class of Nonconvex Programming Problems with Nonlinear Fractional Objectives

In public policy decision making and in capital planning fractional criterion functions occur. For a given set of desirable target values (goals) τ_i, this paper develops an algorithm for solving a nonconvex programming problem of the type: Min_x∈s Max_i{ϕ_i(f_i(x)/g_i(x) − τ_i), i = 1, …, m} where f_i are convex functions, g_i are concave functions over the convex subset S of Rⁿ and ϕ_i are nondecreasing gauge functions. Here ϕ_i(·) is the penalty incurred whenever the fractional objective f_i/g_i deviates from the target value τ_i, the problem is then to choose an x that minimizes the maximum penalty incurred.