Data fitting with signomial programming compatible difference of convex functions

Abstract

Abstract Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking a balance between the computational efficiency of Geometric Programming (GP) and the extensibility of more general methods for optimization. While techniques exist for fitting GP compatible models to data, no models have been proposed that take advantage of the increased modeling flexibility available in SP. Here, a new Difference of Softmax Affine function is constructed by utilizing existing methods of GP compatible fitting in Difference of Convex (DC) functions. This new function class is fit to data in log–log space and becomes either a signomial or a set of signomials upon inverse transformation. Examples presented here include simple test cases in 1D and 2D, and a fit to the performance data of the NACA 24xx family of airfoils. In each case, RMS error is driven to less than 1%.