Abstract
This short note gives the sharp bound for the Q-linear convergence rate of the iterates generated by the steepest descent method with exact line searches when the objective function is strictly convex quadratic.
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References
Forsythe G.E. (1968) On the asymptotic directions of the s-dimensional optimum gradient method. Numer. Math. 11: 57–76
Luenberge D.G. (1968) Optimization by Vector Space Methods. Wiley, New York
Nocedal J., Wright S. (1999) Numerical Optimization. Springer, New York
Sun W.Y., Yuan Y. (2006) Optimization Theory and Methods: Nonlinear Programming. Springer, New York
Yuan, Y.: A Short Note on the Q-linear convergence of the steepest descent method. Research report, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences (2007)
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This work is partially supported by Chinese NSF grant 10831006 and by CAS grant kjcx-yw-s7.
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Yuan, Yx. A short note on the Q-linear convergence of the steepest descent method. Math. Program. 123, 339–343 (2010). https://doi.org/10.1007/s10107-009-0267-8
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DOI: https://doi.org/10.1007/s10107-009-0267-8