Digitalni repozitorijum
Univerziteta u Nišu
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Napredni gradijentni algoritmi za rešavanje problema bezuslovne optimizacije i nelinearnih monotonih sistema jednačina velikih dimenzija
Ivanov, Branislav, 1983-
Stanimirović, Predrag, 1959-
Milovanović, Gradimir V., 1948-
Miladinović, Marko, 1979-
Stanujkić, Dragiša, 1964-
Rajković, Predrag M., 1959-
The doctoral dissertation presents new efficient algorithms for solvingunconstrained optimization problems and monotonic nonlinearsystems of equations. The new algorithms are representatives of theclasses of gradient and conjugate gradient algorithms. Thedissertation presents six new gradient algorithms: two from the classof modified accelerated gradient methods, two from the class ofhybrid modified gradient methods, and two algorithms as aconsequence of the multiple use of line search in gradient methods.From the class of conjugate gradient algorithms, one new three-termmethod, two new mixed conjugate gradient methods, and two newconjugate gradient methods of the Dai-Liao type are presented. Whenit comes to solving systems of nonlinear monotonic equations of largedimensions, a new Dai-Liao type method with improved parameters ispresented. Also, the dissertation presents gradient algorithms forsolving unconstrained optimization problems based on neutrosophy.The convergence analysis and numerical testing of new iterativeschemes confirm the theoretical and practical significance of newgradient and conjugate gradient methods and their algorithms. Theapplication of gradient and conjugate gradient algorithms is given in2D robotic motion control, image restoration processes, andregression analysis.
Bibliografija sa biografijom: str. 215-233. Datum odbrane: 15.10.2025. Computer science and numerical methods; Operational research
Serbian
2025
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