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Projected primal-dual gradient flow of augmented Lagrangian with application to distributed maximization of the algebraic connectivity of a networkPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 98, p. 34-41Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2018. Vol. 98, p. 34-41
##### Keywords [en]

Projected dynamical systems, Semi-definite programming, Distributed optimization
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-239468DOI: 10.1016/j.automatica.2018.09.004ISI: 000449310900005Scopus ID: 2-s2.0-8505380717OAI: oai:DiVA.org:kth-239468DiVA, id: diva2:1265787
#####

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##### Note

##### In thesis

In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with computable projection operation on its tangent cone as well as equality constraints. As a supplement of the analysis in Niederlander and Cortes (2016), we show that the projected dynamical system converges to one of the saddle points and hence finding an optimal solution. Moreover, the problem of distributedly maximizing the algebraic connectivity of an undirected network by optimizing the port gains of each nodes (base stations) is considered. The original semi-definite programming (SDP) problem is relaxed into a nonlinear programming (NP) problem that will be solved by the aforementioned projected dynamical system. Numerical examples show the convergence of the aforementioned algorithm to one of the optimal solutions. The effect of the relaxation is illustrated empirically with numerical examples. A methodology is presented so that the number of iterations needed to reach the equilibrium is suppressed. Complexity per iteration of the algorithm is illustrated with numerical examples.

QC 20181126

Available from: 2018-11-26 Created: 2018-11-26 Last updated: 2019-01-21Bibliographically approved1. Optimizing Networked Systems and Inverse Optimal Control$(function(){PrimeFaces.cw("OverlayPanel","overlay1280925",{id:"formSmash:j_idt720:0:j_idt724",widgetVar:"overlay1280925",target:"formSmash:j_idt720:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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