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

Javier Pena (jfp***at***andrew.cmu.edu)

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.

Keywords: set-valued mapping, block-structure, surjectivity, condition number

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Mathematical Programming 103 (2005) pp. 561--573.

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Entry Submitted: 09/03/2003
Entry Accepted: 09/03/2003
Entry Last Modified: 05/07/2006

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