Two-level primal-dual decomposition technique for large-scale nonconvex optimization problems with constraints
type: Item
instance of: scholarly article
title: Two-level primal-dual decomposition technique for large-scale nonconvex optimization problems with constraints
zbMATH Open document ID: 0713.90059
DOI: 10.1007/BF00940031
author: Bernd Engelmann
author: Piotr Tatjewski
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: The authors are concerned with the separable minimization problem \[ (1)\quad \text{ minimize } f(x)=\sum^{N}_{i=1}f_ i(x_ i)\text{ subject to } h(x)=\sum^{N}_{i=1}h_ i(x_ i)=0, \] \(g_ i(x_ i)\leq 0\) \((i=1,...,N)\), where \(x\in R^ n\), \(x_ i\in R^{n_ i}\), \(n=\sum^{N}_{i=1}n_ i\), \(f_ i:\) \(R^{n_ i}\to R\), \(h_ i:\) \(R^{n_ i}\to R^ m\), \(g_ i:\) \(R^{n_ i}\to R^{\ell_ i}\). To solve (1) by the dual method of decomposition in case of nonconvexity, several techniques have been proposed. Some of them are three-level primal-dual optimization structures or apply to (1) without the inequality constraint \(g_ i(x_ i)\leq 0\). In this paper the authors consider for solving (1) a technique introduced in a previous paper of the first author [Automatica 25, No.2, 233-242 (1989; Zbl 0685.49023)], give a convergence analysis and provide numerical results.
reviewed by: Marco Gaviano
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 49M27
Mathematics Subject Classification ID: 90-08
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C06
zbMATH DE Number: 4174670
zbMATH Keywords: two-level primal-dual decomposition technique
zbMATH Keywords: large-scale nonconvex optimization
zbMATH Keywords: separable minimization
zbMATH Keywords: dual method of decomposition
zbMATH Keywords: nonconvexity
zbMATH Keywords: convergence analysis
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00940031
OpenAlex ID: W2128610608
description: scientific article; zbMATH DE number 4174670