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Distributed Optimization Methods for Large Scale Unconstrained Optimization Problems = = Meтоде дистрибуиране оптимизације за проблеме великихдимензија без ограничења.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Distributed Optimization Methods for Large Scale Unconstrained Optimization Problems =/
其他題名:	Meтоде дистрибуиране оптимизације за проблеме великихдимензија без ограничења.
其他題名:	Meтоде дистрибуиране оптимизације за проблеме великихдимензија без ограничења.
作者:	Malaspina, Greta.
面頁冊數:	1 online resource (214 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-10, Section: B.
Contained By:	Dissertations Abstracts International84-10B.
標題:	Algorithms. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30372663click for full text (PQDT)
ISBN:	9798377685913

Distributed Optimization Methods for Large Scale Unconstrained Optimization Problems = = Meтоде дистрибуиране оптимизације за проблеме великихдимензија без ограничења.
Malaspina, Greta.

Distributed Optimization Methods for Large Scale Unconstrained Optimization Problems =Meтоде дистрибуиране оптимизације за проблеме великихдимензија без ограничења.Meтоде дистрибуиране оптимизације за проблеме великихдимензија без ограничења. - 1 online resource (214 pages)

Source: Dissertations Abstracts International, Volume: 84-10, Section: B.

Thesis (Ph.D.)--University of Novi Sad (Serbia), 2022.

Includes bibliographical references

Many modern applications require networks of computational agents to solve optimization problems in a cooperative manner, while the growing interest in Big Data and machine learning calls for method that are able to solve problems of increasingly large dimension. This poses many challenges in the field of optimization as most classical methods are not suitable for the distributed framework: new algorithms need to be developed, that are able to deal with the practical limitations deriving from the distributed setting. This thesis focuses on distributed methods for large scale optimization.The contributions of this thesis to the area of distributed optimization are the following. First of all, we extend the convergence analysis of a class of existing first-order distributed methods to the case of time-varying networks and uncoordinated time-varying stepsizes. This extension is particularly relevant as changes in the communication network are common in practical applications due to possible technical failures in the communication and the increasing relevance of mobile sensor networks.One of the main issues for distributed optimization is the selection of the stepsize: classical globalization such as line search are not feasible in the multi-agent framework, while employing a fixed stepsize is known to often cause the method to be slow and usually requires the knowledge of the regularity constants of the problem, which can be hard to estimate distributedly. To overcome these issues we propose a distributed Inexact Newton method that relies on an adaptive choice of the stepsize, which can be computed distributedly and, under suitable regularity assumptions, ensures both global convergence and local fast convergence as in the centralized case.Systems of linear equations and large dimensions are a problem of interest by itself and as a part of second-order optimization methods. In general, in each iteration of the second-order method, like Inexact Newton method mentioned above, one has to solve a system of linear equations, either approximately or exactly, to get the search direction. Again, distributed environment represents a challenge. Fixed point methods are a known to be very effective in the centralized framework for linear system of large dimensions. We propose here a class of distributed fixed point methods that works in the distributed setting. We show that such methods converge for both static and time-varying network, achieving convergence results analogous to those that can be proved for the centralized case.Finally, in the last part of the thesis we consider the least square problems of very large dimension motivated by digitalization of cadastral maps. The dimension of the problem represent the main difficulty for classical method while the sparse structure presents an opportunity to be exploited in parallel computational framework. We present an Inexact Levenberg-Marquardt method for sparse least squares problem. The method exploits the underlying structure of the problem to define a fixed-point strategy for the computation of the search direction that is suitable for parallelization. Theoretical analysis is presented and we show both global and fast local convergence under the classical assumptions for least squares problems.All presented methods are implemented, and tested on relevant examples.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798377685913Subjects--Topical Terms:

536374
Algorithms.
Index Terms--Genre/Form:

542853
Electronic books.

Distributed Optimization Methods for Large Scale Unconstrained Optimization Problems = = Meтоде дистрибуиране оптимизације за проблеме великихдимензија без ограничења.
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500 $a Source: Dissertations Abstracts International, Volume: 84-10, Section: B.
500 $a Advisor: Krejic, Natasa;Bellavia, Stefania;Jakovetic, Dusan;Jerinkic, Natasa Krklec.
502 $a Thesis (Ph.D.)--University of Novi Sad (Serbia), 2022.
504 $a Includes bibliographical references
520 $a Many modern applications require networks of computational agents to solve optimization problems in a cooperative manner, while the growing interest in Big Data and machine learning calls for method that are able to solve problems of increasingly large dimension. This poses many challenges in the field of optimization as most classical methods are not suitable for the distributed framework: new algorithms need to be developed, that are able to deal with the practical limitations deriving from the distributed setting. This thesis focuses on distributed methods for large scale optimization.The contributions of this thesis to the area of distributed optimization are the following. First of all, we extend the convergence analysis of a class of existing first-order distributed methods to the case of time-varying networks and uncoordinated time-varying stepsizes. This extension is particularly relevant as changes in the communication network are common in practical applications due to possible technical failures in the communication and the increasing relevance of mobile sensor networks.One of the main issues for distributed optimization is the selection of the stepsize: classical globalization such as line search are not feasible in the multi-agent framework, while employing a fixed stepsize is known to often cause the method to be slow and usually requires the knowledge of the regularity constants of the problem, which can be hard to estimate distributedly. To overcome these issues we propose a distributed Inexact Newton method that relies on an adaptive choice of the stepsize, which can be computed distributedly and, under suitable regularity assumptions, ensures both global convergence and local fast convergence as in the centralized case.Systems of linear equations and large dimensions are a problem of interest by itself and as a part of second-order optimization methods. In general, in each iteration of the second-order method, like Inexact Newton method mentioned above, one has to solve a system of linear equations, either approximately or exactly, to get the search direction. Again, distributed environment represents a challenge. Fixed point methods are a known to be very effective in the centralized framework for linear system of large dimensions. We propose here a class of distributed fixed point methods that works in the distributed setting. We show that such methods converge for both static and time-varying network, achieving convergence results analogous to those that can be proved for the centralized case.Finally, in the last part of the thesis we consider the least square problems of very large dimension motivated by digitalization of cadastral maps. The dimension of the problem represent the main difficulty for classical method while the sparse structure presents an opportunity to be exploited in parallel computational framework. We present an Inexact Levenberg-Marquardt method for sparse least squares problem. The method exploits the underlying structure of the problem to define a fixed-point strategy for the computation of the search direction that is suitable for parallelization. Theoretical analysis is presented and we show both global and fast local convergence under the classical assumptions for least squares problems.All presented methods are implemented, and tested on relevant examples.
520 $a Mnogi savremeni matematicki modeli zahtevaju resavanje problema optimizacije na mrezi racunarskih cvorova u kooperativnom rezimu, dok rastuci interes za velike skupove podataka i masinsko ucenje zahteva metode kojima je moguce resiti probleme sve vecih dimenzija. Vecina klasicnih optimizacionih metoda nije pogodna za primenu u distribuiranom okruzenju, te je potrebno razviti nove metode koji mogu da odgovore na izazove koji poticu iz distribuiranog okruzenja. Ova teza je fokusirana na distribuirane metode za optimizacione probleme velikih dimenzija.Rezultati predavljeni u ovoj tezi su doprinos oblasti distribuirane optimizacije u sledecim aspektima. Prvo je prosirena analiza konvergencije za klasu postojecih distribuiranih metoda prvog reda, za slucaj komunikacionih mreza koje se menjaju u vremenu i za duzine koraka koje se menjaju po vremenu bez koordinacije izmedu komjuterskih cvorova. Ovo prosirenje je od posebnog znacaja u prakticnim primenama gde su promene u komunikacionim mrezama uzrokovane tehnickim problemima ukomunikaciji ili u slucaju sve znacajnijih pokretnih senzorskih mreza.Jedno od glavnih pitanja u metodama distribuirane optimizacije je odredivanje duzine koraka. Naime, klasicne tehnike globalizacije poput linijskog pretrazivanja nisu primenljive u ovom okviru, a primena fiksne duzine koraka cesto dovodi do sporog metoda. Sem toga, primena fiksnog koraka zahteva poznavanje globalnih konstanti koje se ne mogu jednostavno oceniti u distribuiranom okruzenju. Stoga je u tezi predlozen distribuirani priblizan NJutnov metod sa adaptivnom duzinom koraka koja se moze sracunati u distrubiranom okruzenju, a pomocu tako odrdene duzine koraka, uz uobicajene pretpostavke o regularnosti problema, metod je globalno konvergentan i zadrzava lokalni red konvergencije karakteristican za centralizovanu optimizaciju. Sistemi linearnih jednacina velikih dimenzija su izazov i kao nezavisni problemi i kao deo optimizacionih postupaka drugog reda. U opstem slucaju, u svakoj iteraciji metoda drugog reda, poput pribliznog NJutnovog metoda koji je vec pomenut, potrebno je resiti, priblizno ili tacno, sistem linearnih jednacina da bi se odredio pravac pretrazivanja. Distribuirano okruzenje i ovde predstavlja izazov. Metode nepokretne tacke su poznate kao efikasan nacin resavanja sistema linearnih jednacina u centralizovanom okruzenju. Ovde je predstavljena klasa distribuiranih metoda tipa nepokretne tacke koja je prilagodena distribuiranom okruzenju. Pokazano je da postupci predlozenog tipa konvergiraju za staticne i promenljive komunikacione mreze, a rezultati o konvergenciji su analogni rezultatima u centralizovanom slucaju. U poslednjem delu teze je razmtran problem najmanjih kvadrata veoma velike dimenzije motivisan problemom digitalizacije katastarskih mapa. Veoma velika dimenzija problema predstavlja glavni problem za primenu klasicnih metoda, dok je retka struktura problema prirodna mogucnost za primenu paralelnih metoda. U tezi je predstavljen priblizni Levenberg-Markardov metod za resavanje retkih problema najmanjih kvadrata. Retka struktura je iskoriscena kao osnov za definisanje strategije tipa nepokretne tacke kojom se odreduje pravac pretrazivanja na nacin koji je pogodan za paralelizaciju. Predstavljena je teorijska analiza i pokazana globalna i lokalna konvergencija pod klasicnim pretpostavkama za ovaj tip problema.Svi predlozeni metodi su implementirani i testirani na relevantnim test primerima. Numericki rezultati su empirijski potvrdili teorijska tvrdenja. Pored toga, predlozeni metodi su uporedeni sa najznacajnijim postojecim metodama za odgovarajuce klase problema i pokazana je njihova kompetitivnost.
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538 $a Mode of access: World Wide Web
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650 4 $a Communication. $3 524709
650 4 $a Optimization. $3 891104
650 4 $a Linear equations. $3 3683501
650 4 $a Linear algebra. $3 2923381
650 4 $a Computer science. $3 523869
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