A wedge trust region method with self-correcting geometry for derivative-free optimization

Abstract

Recently, some methods for solving optimization problems without derivatives have been proposed. The main part of these methods is to form a suitable model function that can be minimized for obtaining a new iterative point. An important strategy is geometry-improving iteration for a good model, which needs a lot of calculations. Besides, Marazzi and Nocedal (2002) proposed a wedge trust region method for derivative free optimization. In this paper, we propose a new self-correcting geometry procedure with less computational efforts, and combine it with the wedge trust region method. The global convergence of new algorithm is established. The limited numerical experiments show that the new algorithm is efficient and competitive.2010 Mathematics Subject Classification. Primary: 65k05; Secondary: 90c30.