Reduced quasi-Newton method for simultaneous design and optimization
type: Item
instance of: scholarly article
title: Reduced quasi-Newton method for simultaneous design and optimization
zbMATH Open document ID: 1251.90364
author: Adel Hamdi
author: Andreas Griewank
published in: Computational Optimization and Applications
publication date: 2011-06-30T00:00:00Z
review text: The paper deals with a design optimization problem where the constraint is a state equation: (P) min \(f(y,u)\) s.t. \(c(y,u)=0\) where \(y\) denotes the state and \(u\) the design variable. It is assumed that the state \(c(y,u)=0\) can be transformed into a fixed point equation \(y=G(y,u)\). Then (P) is transformed into an equality constrained optimization problem of the form: (PG) min \(f(y,u)\) s.t. \(y=G(y,u)\). The authors use the Lagrangian of (PG) to append the primal iteration with the dual and preconditioned design iterations. The coordination of the three iterative process is guaranteed by using an exact penalty function of double augmented Lagrangian type. Under certain assumptions global convergence of the optimization approach is proved. Finally, some numerical experiments done on a variant of the Bratu problem are presented.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 5915216
zbMATH Keywords: simultaneous analysis and design
zbMATH Keywords: preconditioning
zbMATH Keywords: augmented Lagrangian
zbMATH Keywords: exact penalty function
zbMATH Keywords: global convergence
reviewed by: Francisco Guerra Vazquez
describes a project that uses: ADOL-C
MaRDI profile type: Publication
full work available at URL: s10589-009-9306-x
OpenAlex ID: W2029799595
Wikidata QID: Q57389622
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DBLP publication ID: journals/coap/HamdiG11
DOI: 10.1007/S10589-009-9306-X
description: scientific article; zbMATH DE number 5915216