A Penalty Function Procedure for Sensitivity Analysis of Concave Programs

Given a concave program, consider its optimal objective value as a function of the right-hand side. The behavior of this optimal response function reflects the sensitivity of the objective value to changes in the right-hand side. A scheme involving the optimization of a penalty function is developed for determining the value and gradient of the optimal response function at points within a region of interest. This scheme is then applied to a simple example to illustrate its potential usefulness.