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Weak sharp minima revisited, part II: application to linear regularity and error bounds

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Abstract

The notion of weak sharp minima is an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. It has been studied extensively by several authors. This paper is the second of a series on this subject where the basic results on weak sharp minima in Part I are applied to a number of important problems in convex programming. In Part II we study applications to the linear regularity and bounded linear regularity of a finite collection of convex sets as well as global error bounds in convex programming. We obtain both new results and reproduce several existing results from a fresh perspective.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    James V. Burke

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

    Sien Deng

Authors
  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 our friend and mentor Terry Rockafellar on the occasion of his 70th birthday. He has been our guide in mathematics as well as in the backcountry and waterways of the Olympic and Cascade mountains.

Research supported in part by the National Science Foundation Grant DMS-0203175.

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Burke, J., Deng, S. Weak sharp minima revisited, part II: application to linear regularity and error bounds. Math. Program. 104, 235–261 (2005). https://doi.org/10.1007/s10107-005-0615-2

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