National Repository of Dissertations in Serbia
    • English
    • Српски
    • Српски (Serbia)
  • English 
    • English
    • Serbian (Cyrilic)
    • Serbian (Latin)
  • Login
View Item 
  •   NaRDuS home
  • Универзитет у Новом Саду
  • Природно-математички факултет
  • View Item
  •   NaRDuS home
  • Универзитет у Новом Саду
  • Природно-математички факултет
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Kvazi Njutnovi postupci za probleme stohastičkog programiranja

Quasi Newton Methods for Stochastic Programming Problems

Thumbnail
2016
Disertacija4252.pdf (1.242Mb)
ZoranOvcin.pdf (85.52Kb)
Author
Ovcin, Zoran
Mentor
Krejić, Nataša
Committee members
Lužanin, Zorana
Krejić, Nataša
Uzelac, Zorica
Stojkovska, Irena
Metadata
Show full item record
Abstract
Posmatra se problem minimizacije bez ograničenja. U determinističkom slučaju ti problemi se uspešno rešavaju iterativnim Kvazi Njutnovim postupcima. Ovde se istražuje  stohastički slučaj, kada su poznate vrednosti funkcije cilja i njenog gradijenta na koje je uticao šum. Koristi se novi način određivanja dužina koraka, koji kombinuje metod linijskog pretraživanja i metod stohastičke aproksimacije tako da zadrži dobre osobine oba pristupa i obezbedi veću efikasnost postupka. Metod je testiran u kombinaciji sa više načina izbora pravca u iterativnom postupku. Dokazana je konvergencija novog postupka i testiranjem na velikom broju standardnih test problema pokazana njegova efikasnost. Takođe se za rešavanje problema ekvilibriuma u Neoklasičnoj ekonomiji predlaže i dokazuje konvergencija jednog Fiksnog Njutnovog postupka. U zadatku nalaženja rešenja za niz problema kojima se preciznije modelira slučajni sistem, ovaj Fiksni Njutnov postupak ostvaruje veliku uštedu CPU vremena u odnosu na Nj...utnov metod. U prvom delu teze je dat opšti teoretski uvod. U drugom delu je dat pregled relevantnih rezultata iz posmatranih oblasti zajedno sa dva originalna rezultata. U trećem  delu su dati rezultati numeričkih testova.

The problem under consideration is unconstrained minimization pro-blem. The problem in deterministic case is often solved with Quasi Newton met-hods. In noisy environment, which is considered, new approach for step length along descent direction is used. The new approach combines line search and stoc-hastic  approximation method using good characteristics of both enabling better efficiency. The convergence is proved. New step length is tested with three de-scent directions. Many standard test problems show the efficiency of the met-hod. Also, a new, affordable procedure based on application of the fixed Newton method for a sequence of equilibrium problems generated by simulation is intro-duced. The convergence conditions of the method are derived. The numerical results show a clear difference in the quality of information obtained by solving a sequence of problems if compared with the single equilibrium problem. In the first part general theoretical introduction is given. In the second... part a survey of results from scientific community is given together with original results. The third part contains many numerical tests of new methods that show its efficiency.

Faculty:
Универзитет у Новом Саду, Природно-математички факултет
Date:
19-07-2016
Keywords:
Nelinearna optimizacija / Nonlinear optimization / Quasi-Newton / stochastic optimization. / Kvazi Njutnove metode / stohastička optimizacija.
[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_nardus_6299
URI
https://nardus.mpn.gov.rs/handle/123456789/6299
http://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija146426898759239.pdf?controlNumber=(BISIS)101079&fileName=146426898759239.pdf&id=5830&source=NaRDuS&language=sr
http://www.cris.uns.ac.rs/record.jsf?recordId=101079&source=NaRDuS&language=sr

DSpace software copyright © 2002-2015  DuraSpace
About NaRDus | Contact us

OpenAIRERCUBRODOSTEMPUS
 

 

Browse

All of DSpaceUniversities & FacultiesAuthorsMentorCommittee membersSubjectsThis CollectionAuthorsMentorCommittee membersSubjects

DSpace software copyright © 2002-2015  DuraSpace
About NaRDus | Contact us

OpenAIRERCUBRODOSTEMPUS