TY - JOUR
T1 - Steepest descent method with a generalized Armijo search for quasiconvex functions on Riemannian manifolds
AU - Papa Quiroz, E. A.
AU - Quispe, E. M.
AU - Oliveira, P. Roberto
PY - 2008/5/1
Y1 - 2008/5/1
N2 - This paper extends the full convergence of the steepest descent method with a generalized Armijo search and a proximal regularization to solve minimization problems with quasiconvex objective functions on complete Riemannian manifolds. Previous convergence results are obtained as particular cases and some examples in non-Euclidian spaces are given. In particular, our approach can be used to solve constrained minimization problems with nonconvex objective functions in Euclidian spaces if the set of constraints is a Riemannian manifold and the objective function is quasiconvex in this manifold.
AB - This paper extends the full convergence of the steepest descent method with a generalized Armijo search and a proximal regularization to solve minimization problems with quasiconvex objective functions on complete Riemannian manifolds. Previous convergence results are obtained as particular cases and some examples in non-Euclidian spaces are given. In particular, our approach can be used to solve constrained minimization problems with nonconvex objective functions in Euclidian spaces if the set of constraints is a Riemannian manifold and the objective function is quasiconvex in this manifold.
KW - Quasiconvex functions
KW - Riemannian manifolds
KW - Steepest descent method
UR - http://www.scopus.com/inward/record.url?scp=38749142181&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2007.10.010
DO - 10.1016/j.jmaa.2007.10.010
M3 - Artículo
AN - SCOPUS:38749142181
SN - 0022-247X
VL - 341
SP - 467
EP - 477
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -