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 R n 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.

• 저널Management Science · 31(7) · 847–851
• 토픽Optimization and Mathematical Programming · Control and Systems Engineering
• DOI10.1287/mnsc.31.7.847
• 저자R. Jagannathan