On the block-structured distance to non-surjectivity of sublinear mappings
Javier Pena (jfpandrew.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.
Entry Submitted: 09/03/2003
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