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Global convergence result for conjugate gradient methods. (English) Zbl 0794.90063

Summary: Conjugate gradient optimization algorithms depend on the search directions, \(s^{(1)}= -g^{(1)}\), \(s^{(k+1)}=- g^{(k+1)}+ \beta^{(k)}s^{(k)}\), \(k\geq 1\), with different methods arising from different choices for the scalar \(\beta^{(k)}\). In this note, conditions are given on \(\beta^{(k)}\) to ensure global convergence of the resulting algorithms.

MSC:

90C30 Nonlinear programming
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