Nalazite se na CroRIS probnoj okolini. Ovdje evidentirani podaci neće biti pohranjeni u Informacijskom sustavu znanosti RH. Ako je ovo greška, CroRIS produkcijskoj okolini moguće je pristupi putem poveznice www.croris.hr
izvor podataka: crosbi

A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set (CROSBI ID 237450)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Scitovski, Rudolf A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set // Journal of global optimization, 68 (2017), 4; 713-727. doi: 10.1007/S10898-017-0510-4

Podaci o odgovornosti

Scitovski, Rudolf

engleski

A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set

In this paper, we consider a global optimization problem for a symmetric Lipschitz continuous function $g : [a, b]^k \to \mathbb{; ; ; ; R}; ; ; ; $ whose domain $[a, b]^k \in \mathbb{; ; ; ; R}; ; ; ; ^k$ consists of k! hypertetrahedrons of the same size and shape, in which function g attains equal values. A global minimum can therefore be searched for in one hypertetrahedron only, but then this becomes a global optimization problem with linear constraints. Apart from that, some known global optimization algorithms in standard form cannot be applied to solving the problem. In this paper, it is shown how this global optimization problem with linear constraints can easily be transformed into a global optimization problem on hypercube $[0, 1]^k$, for the solving of which an applied DIRECT algorithm in standard form is possible. This approach has a somewhat lower efficiency than known global optimization methods for symmetric Lipschitz continuous functions (such as SymDIRECT or DISIMPL), but, on the other hand, this method allows for the use of publicly available and well developed computer codes for solving a global optimization problem on hypercube $[0, 1]^k$ (e.g. the DIRECT algorithm). The method is illustrated and tested on standard symmetric functions and very demanding center-based clustering problems for the data that have only one feature. An application to the image segmentation problem is also shown.

Symmetric function ; Lipschitz continuous function ; Global optimization ; DIRECT ; Sym DIRECT ; DISIMPL ; Center-based clustering

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

Podaci o izdanju

68 (4)

2017.

713-727

objavljeno

0925-5001

1573-2916

10.1007/S10898-017-0510-4

Povezanost rada

Matematika

Poveznice
Indeksiranost