2 research outputs found

    A note on error bounds for convex and nonconvex programs

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    Title from caption. "March, 1998"--Cover. "June 1997. -- Modified in February 1998 (formerly LIDS-P-2393)"Includes bibliographical references (p. 13).Supported in part by the National Science Foundation. 9300494-DMIby Dimitri P. Bertsekas

    Error Estimates and Lipschitz Constants for Best Approximation in Continuous Function Spaces

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    We use a structural characterization of the metric projection PG(f), from the continuous function space to its one-dimensional subspace G, to derive a lower bound of the Hausdorff strong unicity constant (or weak sharp minimum constant) for PG and then show this lower bound can be attained. Then the exact value of Lipschitz constant for PG is computed. The process is a quantitative analysis based on the Gâteaux derivative of PG, a representation of local Lipschitz constants, the equivalence of local and global Lipschitz constants for lower semicontinuous mappings, and construction of functions
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