Application of the Parabola Method in Nonconvex Optimization
Anton Kolosnitsyn,
Oleg Khamisov,
Eugene Semenkin,
Vladimir Nelyub
Affiliations
Anton Kolosnitsyn
Department of Applied Mathematics, Melentiev Energy Systems Institute, Lermontov St. 130, 664033 Irkutsk, Russia
Oleg Khamisov
Department of Applied Mathematics, Melentiev Energy Systems Institute, Lermontov St. 130, 664033 Irkutsk, Russia
Eugene Semenkin
Scientific and Educational Center “Artificial Intellegence Technologies”, Bauman Moscow State Technical University, 2nd Baumanskaya, Str. 5, 105005 Moscow, Russia
Vladimir Nelyub
Scientific and Educational Center “Artificial Intellegence Technologies”, Bauman Moscow State Technical University, 2nd Baumanskaya, Str. 5, 105005 Moscow, Russia
We consider the Golden Section and Parabola Methods for solving univariate optimization problems. For multivariate problems, we use these methods as line search procedures in combination with well-known zero-order methods such as the coordinate descent method, the Hooke and Jeeves method, and the Rosenbrock method. A comprehensive numerical comparison of the obtained versions of zero-order methods is given in the present work. The set of test problems includes nonconvex functions with a large number of local and global optimum points. Zero-order methods combined with the Parabola method demonstrate high performance and quite frequently find the global optimum even for large problems (up to 100 variables).
