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A penalty method for the approximation of projections over cones in Hilbert spaces

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Abstract

Given a closed convex coneK in a Hilbert spaceH and a vectoru 0 ∈H, a penalty method is built up in order to approximate the projection ofu 0 over the polar coneK * ofK, without making use of the inverse transform of the canonical mapping ofH into its dual spaceH′. Such method is outlined in n0 1, 2. In n03 a complete analysis of the errors of the method is explained. In n04 the method is applied to find error bounds for the numerical approximation of the projection ofu 0 onK.

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  1. Istituto Matematico dell'Università, Roma

    A. Fusciardi

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  1. A. Fusciardi
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Fusciardi, A. A penalty method for the approximation of projections over cones in Hilbert spaces. Calcolo 14, 205–218 (1977). https://doi.org/10.1007/BF02576811

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  • DOI: https://doi.org/10.1007/BF02576811

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