An algorithm for separable nonlinear minimax problems.

We consider a minimax problem in which each term of the objective function is a monotone decreasing, invertible function of a single decision variable. The objective is to minimize the maximum term subject to a set of linear constraints with only nonnegative coefficients. Further, all decision variables must be nonnegative, and upper bounds can be imposed. Such problems have applications in numerous resource allocation problems in which limited resources need to be allocated among competing activities so as to balance given cost functions. For example, in production planning, resources are often allocated among competing product lines so that the maximum weighted deviation from given demands will be minimized.