Globally Convergent Three‐Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization

Globally Convergent Three‐Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization

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Article ID: iaor20123934
Volume: 153
Issue: 3
Start Page Number: 733
End Page Number: 757
Publication Date: Jun 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: heuristics
Abstract:

In this paper, we propose a three‐term conjugate gradient method based on secant conditions for unconstrained optimization problems. Specifically, we apply the idea of Dai and Liao (2001) to the three‐term conjugate gradient method proposed by Narushima et al. (2011). Moreover, we derive a special‐purpose three‐term conjugate gradient method for a problem, whose objective function has a special structure, and apply it to nonlinear least squares problems. We prove the global convergence properties of the proposed methods. Finally, some numerical results are given to show the performance of our methods.

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