caa a22 4500 463170032 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s10957-006-9123-7 doi (NATIONALLICENCE)springer-10.1007/s10957-006-9123-7 Armand P. Maître de Conférences, Université de Limoges, Limoges, France aut Modification of the Wolfe Line Search Rules to Satisfy the Descent Condition in the Polak-Ribière-Polyak Conjugate Gradient Method [Elektronische Daten] [P. Armand] This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests are presented. Springer Science + Business Media, Inc., 2006 Conjugate gradient method nationallicence line search algorithm nationallicence unconstrained optimization nationallicence Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/2(2007-02-01), 287-305 0022-3239 132:2<287 2007 132 10957 https://doi.org/10.1007/s10957-006-9123-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-006-9123-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Armand P. Maître de Conférences, Université de Limoges, Limoges, France aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/2(2007-02-01), 287-305 0022-3239 132:2<287 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer