<p>The linear complementarity problems (LCP) arise from linear or quadratic programming, or from a variety of other particular application problems, like boundary problems, network equilibrium problems,contact problems, market equilibria problems, bimatrix games etc. Recently, many people have focused on the solver of LCP with a matrix having some kind of special property, for example, when this matrix is an H+-matrix, since this property is a sufficient condition for the existence and uniqueness of the soluition of LCP. Generally speaking, solving LCP can be approached from two essentially different perspectives. One of them includes the use of so-called direct methods, in the literature also known under the name pivoting methods. The other, and from our perspective - more interesting one, which we actually focus on in this thesis,<br />is the iterative approach. Among the vast collection of iterative solvers,our choice was one particular class of modulus based iterative methods.Since the subclass of modulus based-methods is again diverse in some sense, it can be specialized even further, by the introduction and the use of matrix splittings. The main goal of this thesis is to use the theory of H -matrices for proving convergence of the modulus-based multisplit-ting methods, and to use this new technique to analyze some important properties of iterative methods once the convergence has been guaranteed.</p> / <p>Problemi linearne komplementarnosti (LCP) se javljaju kod problema linearnog i kvadratnog programiranja i kod mnogih drugih problema iz prakse, kao što su, na primer, problemi sa graničnim slojem, problemi mrežnih ekvilibrijuma, kontaktni problemi, problemi određivanja tržišne ravnoteže, problemi bimatričnih igara i mnogi drugi. Ne tako davno, veliki broj autora se bavio razvijanjem postupaka za rešavanje LCP sa matricom koja ispunjava neko specijalno svojstvo, na primer, da pripada klasi H+-matrica, budući da je dobro poznato da je ovaj uslov dovoljan da obezbedi egzistenciju i jedinstvenost rešenja LCP. Uopšteno govoreći, rešavanju LCP moguce je pristupiti dvojako. Prvi pristup podrazumeva upotrebu takozvanih direktnih metoda, koje su u literaturi poznate i pod nazivom metode pivota. Drugoj kategoriji, koja je i sa stanovišta ove teze interesantna, pripadaju iterativni postupci. S obzirom da je ova kategorija izuzetno bogata, mi smo se opredelili za jednu od najznačajnijih varijanti, a to je modulski iterativni postupak. Međutim, ni ova odrednica nije dovoljno adekvatna, budući da modulski postupci obuhvataju nekolicinu različitih pravaca. Zato smo se odlučili da posmatramo postupke koji se zasnivaju na razlaganjima ali i višestrukim razlaganjima matrice. Glavni cilj ove doktorske disertacije jeste upotreba teorije H -matrica u teoremama o konvergenciji modulskih metoda zasnovanih na multisplitinzima matrice i korišćenje ove nove tehnike, sa ciljem analize bitnih osobina, nakon što je konvergencija postupka zagarantovana.</p>
| Identifer | oai:union.ndltd.org:uns.ac.rs/oai:CRISUNS:(BISIS)110168 |
| Date | 18 March 2019 |
| Creators | Saeed Aboglida Saeed Abear |
| Contributors | Cvetković Ljiljana, Nedeljkov Marko, Kostić Vladimir, Doroslovački Ksenija |
| Publisher | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, University of Novi Sad, Faculty of Sciences at Novi Sad |
| Source Sets | University of Novi Sad |
| Language | English |
| Detected Language | English |
| Type | PhD thesis |
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