Conjugate gradient methods based on secant conditions that generate descent search directions for unconstrained optimization

• Autores: Yasushi Narushima, Hiroshi Yabe
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 236, Nº 17, 2012, págs. 4303-4317
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.01.036
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• Resumen

  • Conjugate gradient methods have been paid attention to, because they can be directly applied to large-scale unconstrained optimization problems. In order to incorporate second order information of the objective function into conjugate gradient methods, Dai and Liao (2001) proposed a conjugate gradient method based on the secant condition. However, their method does not necessarily generate a descent search direction. On the other hand, Hager and Zhang (2005) proposed another conjugate gradient method which always generates a descent search direction.

    In this paper, combining Dai�Liao�s idea and Hager�Zhang�s idea, we propose conjugate gradient methods based on secant conditions that generate descent search directions.

    In addition, we prove global convergence properties of the proposed methods. Finally, preliminary numerical results are given.