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Efficient hybrid conjugate gradient techniques. (English) Zbl 0666.90063
Descent properties and global convergence proofs are given for a new hybrid conjugate gradient algorithm. Computational results for this algorithm are also given and compared with those of the Fletcher-Reeves and the Polak-Ribière methods, showing a considerable improvement over the latter two methods. We also give new criteria for restarting conjugate gradient algorithms that prove to be computationally very efficient. These criteria provide a descent property and global convergence for any conjugate gradient algorithm using a nonnegative update β.
Reviewer: D.Touati-Ahmed
MSC:
90C30Nonlinear programming
65K05Mathematical programming (numerical methods)
90C52Methods of reduced gradient type
49M37Methods of nonlinear programming type in calculus of variations
References:
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[4]Polak, E., andRibière, G.,Note sur la Convergence des Méthodes de Directions Conjuguées, Revue Française, Information et Recherche Opérationelle, Vol. 16, pp. 35-43, 1969.
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[8]Powell, M. J. D.,Convergence Properties of Algorithms for Nonlinear Optimization, Report No. DAMTP 1985/NA1, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England, 1985.
[9]Shanno, D. F.,Globally Convergent Conjugate Gradient Algorithms, Mathematical Programming, Vol. 33, pp. 61-67, 1985. · Zbl 0579.90079 · doi:10.1007/BF01582011
[10]Touati-Ahmed, D., andStorey, C.,Globally Convergent Hybrid Conjugate Gradient Methods, Mathematics Research Report No. 196, Department of Mathematics, Loughborough University of Technology, Loughborough, Leicestershire, England, 1986.
[11]Wolfe, M. A.,Numerical Methods for Unconstrained Optimization: An Introduction, Van Nostrand Reinhold, London, England, 1978.
[12]Touati-Ahmed, D.,Efficient Hybrid Conjugate-Gradient Techniques, PhD Thesis, Department of Mathematics, Loughborough University of Technology, Loughborough, Leicestershire, England, 1988.