Nonsmooth Optimization Techniques on Riemannian Manifolds |
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Authors: | S. Hosseini M. R. Pouryayevali |
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Affiliation: | 1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
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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. |
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