A Nonlinear Conjugate Gradient Method Using Inexact First-Order Information

Tiantian Zhao () and Wei Hong Yang ()
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Tiantian Zhao: Fudan University
Wei Hong Yang: Fudan University

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 2, No 3, 502-530

Abstract: Abstract Conjugate gradient methods are widely used for solving nonlinear optimization problems. In some practical problems, we can only get approximate values of the objective function and its gradient. It is necessary to consider optimization algorithms that use inexact function evaluations and inexact gradients. In this paper, we propose an inexact nonlinear conjugate gradient (INCG) method to solve such problems. Under some mild conditions, the global convergence of INCG is proved. Specifically, we establish the linear convergence of INCG when the objective function is strongly convex. Numerical results demonstrate that, compared to the state-of-the-art algorithms, INCG is an effective method.

Keywords: Nonlinear conjugate gradient methods; Inexact first-order information; Inexact gradient method; Global convergence; 90C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02243-y

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