Journal of Optimization Theory and Applications

, Volume 158, Issue 2, pp 328–342 | Cite as

Nonsmooth Optimization Techniques on Riemannian Manifolds



We present the notion of weakly metrically regular functions on manifolds. Then, a sufficient condition for a real valued function defined on a complete Riemannian manifold to be weakly metrically regular is obtained, and two optimization problems on Riemannian manifolds are considered. Moreover, we present a generalization of the Palais–Smale condition for lower semicontinuous functions defined on manifolds. Then, we use this notion to obtain necessary conditions of optimality for a general minimization problem on complete Riemannian manifolds.


Ekeland variational principle Contingent cone Metric regularity Generalized gradient Riemannian manifolds 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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