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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 the following preview by Y. F. Hu and the second author.]

Reviewer: Y.Liu

90C30Nonlinear programming
90-08Computational methods (optimization)
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