Efficient generalized conjugate gradient algorithms. I: Theory. (English) Zbl 0702.90077

The effect of inexact line search on conjugacy is studied in unconstrained optimization. A generalized conjugate gradient method based on this effect is proposed and shown to have global convergence for a twice continuously differentiable function with a bounded level set.
For part II see [Y. F. Hu and second author, J. Optim. Theory Appl. 69, No. 1, 139–152 (1991; Zbl 0724.90068)].
Reviewer: Y.Liu


90C30 Nonlinear programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming


Zbl 0724.90068
Full Text: DOI


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