Resizing: Predicting a New Geometric Programming Optimum as Coefficients Vary

Abstract

Imagine that an optimal solution is available for a constrained geometric program, and suppose one wishes a satisfactory solution for greatly different values of some of the coefficients. An estimate can be constructed by using the values of the dual variables for the old optimum in the invariance conditions for the new problem. Although these are inconsistent except at the precise optimum, a unique primal solution can easily be generated from them by the method of least squares with individual equations weighted by the value of the corresponding dual variable. The matrix equations for these linear operations are derived and applied to a well-known merchant fleet design problem. The predictions are remarkably accurate—1.4 percent error for a 100 percent coefficient change.