Document Type

Article

Publication Date

2026

DOI

10.3390/designs10010011

Publication Title

Designs

Volume

10

Issue

1

Pages

11

Abstract

Design optimization is a computational tool that can enable a designer to investigate the effectiveness of a design concept in an organized format. However, this design process requires the design variables, constraints, and objective function to be properly defined and expressed in mathematical forms. Post-optimality analysis thus becomes a necessary step to investigate different variations in the problem formulation and parameters to ensure that optimization produces a stable and trustworthy outcome. One efficient way to achieve this aim is to compute the local derivative of the optimized objective function with respect to the optimization problem parameters, such as bounds on the constraints and the material properties in the state equation. This method is referred to as post-optimality sensitivity analysis. In this study, we derived the post-optimal sensitivity equation to explicitly include the derivatives of state variables with respect to problem parameters and to broaden its applications to minimax and goal attainment design optimization problems.

Rights

© 2026 by the authors.

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) License.

Data Availability

Article states: "Data and detailed equation derivations are available upon request."

Original Publication Citation

Hou, G., & DeGroff, J. (2026). Gradient-based, post-optimality sensitivity analysis with respect to parameters of state equations. Designs, 10(1), Article 11. https://doi.org/10.3390/designs10010011

ORCID

0000-0002-7352-1099 (Hou)

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