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

Abstract

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