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On the block-structured distance to non-surjectivity of sublinear mappings

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Abstract.

We show that the block-structured distance to non-surjectivity of a set-valued sublinear mapping equals the reciprocal of a suitable block-structured norm of its inverse. This gives a natural generalization of the classical Eckart and Young identity for square invertible matrices.

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Authors and Affiliations

  1. Graduate School of Industrial Administration, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213-3890, USA

    Javier Peña

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  1. Javier Peña
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Correspondence to Javier Peña.

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Mathematics Subject Classification (1991): 15A12, 65F35, 65F50, 90C25

Supported by NSF grant CCF-0092655

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Peña, J. On the block-structured distance to non-surjectivity of sublinear mappings. Math. Program. 103, 561–573 (2005). https://doi.org/10.1007/s10107-004-0514-y

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  • DOI: https://doi.org/10.1007/s10107-004-0514-y

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