Open Problems in Nonlinear Conjugate Gradient Algorithms for Unconstrained Optimization

Neculai Andrei
nandrei@ici.ro
National Institute for Research and Development in Informatics, ICI Bucharest
Academy of Romanian Scientists of Bucharest

Abstract: The paper presents some open problems associated to the nonlinear conjugate gradient algorithms for unconstrained optimization. Mainly, these problems refer to the initial direction, the conjugacy condition, the steplength computation, new formula for conjugate gradient parameter computation based on function’s values, the influence of accuracy of line search procedure, how we can take the problem’s structure on conjugate gradient algorithms, how we can consider the second order information in these algorithms, what the best restart procedure is, what the best hybrid conjugate gradient algorithm is, scaled conjugate gradient algorithms, what the best stopping criterion in conjugate gradient algorithms is etc.

Keywords: Conjugate gradient, conjugacy condition, restart, second order information, structure, hybrid conjugate gradient, scaling.

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CITE THIS PAPER AS:
Neculai Andrei, Open Problems in Nonlinear Conjugate Gradient Algorithms for Unconstrained Optimization, Romanian Journal of Information Technology and Automatic Control, ISSN 1220-1758, vol. 19(1), pp. 5-14, 2009.