Global optimization with unknown Lipschitz constant / von Matthias Ulrich Horn

We study the global optimization problem, i.e., for a real-valued and bounded function f we are interested in a point x of the domain whose function value f(x) is close to the infimum inf f. We consider the case that f is d-variate, Lipschitz, and, in a certain sense, does not increase too slowly in a neighborhood of the global minimizer(s). We give two contributions: We show that for an optimal method adaptiveness is necessary and that randomization (Monte Carlo) yields no further advantage. We present a method that is universal in the following sense: This algorithm has the optimal rate of convergence even if neither the Lipschitz constant nor any other function parameter is known.

Saved in:
Person: Horn, Matthias Ulrich [Author]
Corporate Author: Friedrich-Schiller-Universität Jena [Degree granting institution]
Format: Book
Language(s):English
Publication:Jena, 2005
Printing place:Jena
Dissertation:Jena, Univ., Diss., 2005
Subjects:Globale Optimierung > Algorithmus > Universalität > Lipschitz-Stetigkeit
Type of content:Hochschulschrift
Related resources:Erscheint auch als Online-Ausgabe: Global optimization with unknown Lipschitz constant
Physical description:VIII, 81 S. : graph. Darst. ; 29 cm
Basic Classification: 31.76 Numerische Mathematik