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Gap functions and globally projected differential inclusions on Riemannian manifolds

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Abstract

We consider variational inequality problems on complete Riemannian manifolds and we introduce the globally projected differential inclusions associated with these problems. Then we show that every solution of a variational inequality problem is an equilibrium point of the associated globally projected differential inclusion. Finally, we prove that on a complete Riemannian manifold with nonpositive curvature, one can find a gap function for the variational inequality problem.

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Authors and Affiliations

  1. Department of Mathematics, University of Isfahan, P.O.Box 81745-163, Isfahan, Iran

    Hajar Radmanesh

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  1. Hajar Radmanesh
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Correspondence to Hajar Radmanesh.

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Radmanesh, H. Gap functions and globally projected differential inclusions on Riemannian manifolds. Rend. Circ. Mat. Palermo, II. Ser 68, 315–327 (2019). https://doi.org/10.1007/s12215-018-0361-y

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  • DOI: https://doi.org/10.1007/s12215-018-0361-y

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