An Algorithm for a Class of Nonconvex Programming Problems with Nonlinear Fractional Objectives
针对公共政策决策和资本规划中出现的分数准则函数，提出一种算法，用于求解在凸集上最小化最大惩罚的非凸规划问题，其中惩罚由分数目标与目标值的偏差通过非递减规范函数定义。
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.