Advanced gradient algorithms for solving unconstrained optimization problems and monotonic nonlinear systems of equations of large dimensions

[B. D. Ivanov]

233 str.

Bibliografija sa biografijom: str. 215-233.

Computer science and numerical methods; Operational research

The doctoral dissertation presents new efficient algorithms for solving unconstrained optimization problems and monotonic nonlinear systems of equations. The new algorithms are representatives of the classes of gradient and conjugate gradient algorithms. The dissertation presents six new gradient algorithms: two from the class of modified accelerated gradient methods, two from the class of hybrid modified gradient methods, and two algorithms as a consequence of the multiple use of line search in gradient methods. From the class of conjugate gradient algorithms, one new three-term method, two new mixed conjugate gradient methods, and two new conjugate gradient methods of the Dai-Liao type are presented. When it comes to solving systems of nonlinear monotonic equations of large dimensions, a new Dai-Liao type method with improved parameters is presented. Also, the dissertation presents gradient algorithms for solving unconstrained optimization problems based on neutrosophy. The convergence analysis and numerical testing of new iterative schemes confirm the theoretical and practical significance of new gradient and conjugate gradient methods and their algorithms. The application of gradient and conjugate gradient algorithms is given in 2D robotic motion control, image restoration processes, and regression analysis.

nelinearna optimizacija, matematičko programiranje, algoritmi, gradijentni metodi, konjugovano gradijentni metodi, metodi linijskog pretraživanja, sistemi nelinearnih monotonih jednačina, neutrosofija

nonlinear optimization, mathematical programming, algorithms, gradient methods, conjugate gradient methods, line search methods, systems of monotone nonlinear equations, neutrosophy

004+[005.31+519.6](043.3)

P160; P170

Tekst