A sensitivity interpretation of adjoint variables in optimal design
type: Item
instance of: scholarly article
title: A sensitivity interpretation of adjoint variables in optimal design
zbMATH Open document ID: 0538.73112
DOI: 10.1016/0045-7825(85)90068-4
author: Ashok D. Belegundu
author: Jasbir S. Arora
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1985-01-01T00:00:00Z
review text: The adjoint method of computing derivatives of cost and constraint functions with respect to design variables requires the calculation of certain adjoint variables. Until now, the adjoint variables have been looked upon only as some intermediate vectors needed to calculate design derivatives. In this paper, they are shown to have an important significance. They represent the sensitivity of the cost and constraint functions with respect to the loading or forcing function in the design problem. A sensitivity theorem for the adjoint variables is presented for structural, mechanical dynamic, and distributed parameter systems. These results offer some immediate practical advantages, such as a method for computing influence coefficients for structural systems, and a method for verifying (debugging) the analytical calculation of adjoint variables in development of a computer code.
Mathematics Subject Classification ID: 74P99
Mathematics Subject Classification ID: 93B35
zbMATH DE Number: 3856593
zbMATH Keywords: derivatives of cost and constraint functions
zbMATH Keywords: respect to design variables
zbMATH Keywords: adjoint variables
zbMATH Keywords: sensitivity of the cost and constraint functions
zbMATH Keywords: respect to the loading or forcing function
zbMATH Keywords: sensitivity theorem
zbMATH Keywords: structural, mechanical dynamic, and distributed parameter systems
MaRDI profile type: Publication
full work available at URL: 0045-7825(85)90068-4
OpenAlex ID: W1981296455
cites work: Q3865911
cites work: An approach to nonlinear programming
cites work: Q5566063
cites work: The adjoint method for determining influence lines
description: scientific article; zbMATH DE number 3856593