Search Procedure Exploiting Locally Regularized Objective Approximation. A Convergence Theorem for Direct Search Algorithms

Autor:	Marek Bazan
Rok vydání:	2010
Předmět:	Line search Convergence (routing) Search procedure Direct search Radial basis function Extension (predicate logic) Element (category theory) Algorithm Mathematics
Zdroj:	Computational Intelligence in Optimization ISBN: 9783642127748
DOI:	10.1007/978-3-642-12775-5_4
Popis:	The Search Procedure Exploiting Locally Regularized Objective Approximation is a method to speed-up local optimization processes in which the objective function evaluation is expensive. It was introduced in [1] and further developed in [2]. In this paper we present the convergence theorem of the method. The theorem is proved for the EXTREM [6] algorithm but applies to any Gauss-Siedle algorithm that uses sequential quadratic interpolation (SQI) as a line search method. After some extension it can also be applied to conjugate direction algorithms. The proof is based on the Zangwill theory of closed transformations. This method of the proof was chosen instead of sufficient decrease approach since the crucial element of the presented proof is an extension of the SQI convergence proof from [14] which is based on this approach.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1750074bbf3bb1285265503a27193570 https://doi.org/10.1007/978-3-642-12775-5_4 Zobrazit plný text záznamu