@article{karcher2022data,
title = {Data Fitting with Signomial Programming Compatible Difference of Convex Functions},
author = {Karcher, Cody J.},
year = {2022},
month = {April},
day = {7},
urldate = {2022-01-30},
journal = {Optimization and Engineering},
issn = {1389-4420},
doi = {10.1007/s11081-022-09717-4},
keywords = {Difference of Convex and Mathematical Modeling},
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\%.}
}