surjectivity

The structured distance to ill-posedness for conic systems

  • Adrian Lewis
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    An important measure of conditioning of a conic linear system is the size of the smallest structured perturbation making the system ill-posed. We show that this measure is unchanged if we restrict to perturbations of low rank. We thereby derive a broad generalization of the classical Eckart-Young result characterizing the distance to ill-posedness for a … Read more

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

  • Javier F. Peña
    • Categories Convex Optimization, Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , ,

    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. CitationMathematical Programming 103 (2005) pp. 561–573.