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Weak sharp minima revisited, Part III: error bounds for differentiable convex inclusions

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Abstract

The notion of weak sharp minima unifies a number of important ideas in optimization. Part I of this work provides the foundation for the theory of weak sharp minima in the infinite-dimensional setting. Part II discusses applications of these results to linear regularity and error bounds for nondifferentiable convex inequalities. This work applies the results of Part I to error bounds for differentiable convex inclusions. A number of standard constraint qualifications for such inclusions are also examined.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box # 354350, Seattle, WA, 98195–4350, USA

    James V. Burke

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA

    Sien Deng

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  1. James V. Burke
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  2. Sien Deng
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Correspondence to James V. Burke.

Additional information

We dedicate this paper to Professor A. Auslender on the occasion of his 65th birthday. We, and the optimization community at large, have greatly profited from the deep insight and intuition Professor Auslender has brought to the subject over his many years of his service.

J. V. Burke’s research was supported in part by the National Science Foundation Grant No. DMS-0505712.

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Burke, J.V., Deng, S. Weak sharp minima revisited, Part III: error bounds for differentiable convex inclusions. Math. Program. 116, 37–56 (2009). https://doi.org/10.1007/s10107-007-0130-8

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