caa a22 4500 463170067 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s10957-006-9081-0 doi (NATIONALLICENCE)springer-10.1007/s10957-006-9081-0 Yang Y. Senior Principal Satellite Control Engineer, Orbital Sciences Corporation, Dulles, Virginia, USA aut Globally Convergent Optimization Algorithms on Riemannian Manifolds: Uniform Framework for Unconstrained and Constrained Optimization [Elektronische Daten] [Y. Yang] This paper proposes several globally convergent geometric optimization algorithms on Riemannian manifolds, which extend some existing geometric optimization techniques. Since any set of smooth constraints in the Euclidean space R n (corresponding to constrained optimization) and the R n space itself (corresponding to unconstrained optimization) are both special Riemannian manifolds, and since these algorithms are developed on general Riemannian manifolds, the techniques discussed in this paper provide a uniform framework for constrained and unconstrained optimization problems. Unlike some earlier works, the new algorithms have less restrictions in both convergence results and in practice. For example, global minimization in the one-dimensional search is not required. All the algorithms addressed in this paper are globally convergent. For some special Riemannian manifold other than R n , the new algorithms are very efficient. Convergence rates are obtained. Applications are discussed. Springer Science+Business Media, Inc., 2006 Riemannian manifolds nationallicence globally convergent optimization nationallicence nonlinear programming nationallicence geodesics nationallicence Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/2(2007-02-01), 245-265 0022-3239 132:2<245 2007 132 10957 https://doi.org/10.1007/s10957-006-9081-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-006-9081-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Yang Y. Senior Principal Satellite Control Engineer, Orbital Sciences Corporation, Dulles, Virginia, USA 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), 245-265 0022-3239 132:2<245 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer