Mathematical Programming

, Volume 116, Issue 1–2, pp 37–56 | Cite as

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

  • James V. BurkeEmail author
  • Sien Deng


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.


Weak sharp minima Convex inclusion Affine convex inclusion Constraint qualification Error bounds Calmness 

Mathematics Subject Classification (2000)

90C25 90C31 49J52 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

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