Nonsmooth Optimization Techniques on Riemannian Manifolds

S. Hosseini () and M. R. Pouryayevali ()
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S. Hosseini: Institute for Research in Fundamental Sciences (IPM)
M. R. Pouryayevali: Institute for Research in Fundamental Sciences (IPM)

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 2, No 2, 328-342

Abstract: Abstract 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.

Keywords: Ekeland variational principle; Contingent cone; Metric regularity; Generalized gradient; Riemannian manifolds (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-012-0250-z

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