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

Autor:	Bazan, Marek
Zdroj:	Computational Intelligence in Optimization; 2010, p73-103, 31p
Abstrakt:	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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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