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Global error bounds for piecewise convex polynomials

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In this paper, by examining the recession properties of convex polynomials, we provide a necessary and sufficient condition for a piecewise convex polynomial to have a Hölder-type global error bound with an explicit Hölder exponent. Our result extends the corresponding results of Li (SIAM J Control Optim 33(5):1510–1529, 1995) from piecewise convex quadratic functions to piecewise convex polynomials.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia

    Guoyin Li

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  1. Guoyin Li
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Correspondence to Guoyin Li.

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This research was partially supported by a grant from the Australian Research Council.

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Li, G. Global error bounds for piecewise convex polynomials. Math. Program. 137, 37–64 (2013). https://doi.org/10.1007/s10107-011-0481-z

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