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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 [Y. F. Hu and second author, J. Optim. Theory Appl. 69, No. 1, 139–152 (1991; Zbl 0724.90068)].
Reviewer: Y.Liu

MSC:

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

Citations:

Zbl 0724.90068
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References:

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[9] Hu, Y. F., andStorey, C.,Efficient Generalized Conjugate Gradient Algorithms, Part 2: Implementation, Journal of Optimization Theory and Applications, Vol. 69, No. 1, pp. 139-152, 1991. · Zbl 0724.90068
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