Data fitting with signomial programming compatible difference of convex functions

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 mode...

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Bibliographic Details
Published in:Optimization and engineering Vol. 24; no. 2; pp. 973 - 987
Main Author: Karcher, Cody J.
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2023
Subjects:
Control
Engineering
Environmental Management
Financial Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Research Article
Systems Theory
Signomial programming
Log-log convexity
Difference of convex functions
Data fitting
ISSN:1389-4420, 1573-2924
Online Access:Get full text
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Summary: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%.
ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-022-09717-4