Math. Program., Ser. B (2009) 116:37–56 DOI 10.1007/s10107-007-0130-8 FULL LENGTH PAPER Weak sharp minima revisited, Part III: error bounds for differentiable convex inclusions James V. Burke · Sien Deng Received: 15 August 2005 / Accepted: 4 April 2006 / Published online: 28 April 2007 © Springer-Verlag 2007 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 re- sults to linear regularity and error bounds for nondifferentiable convex inequalities. This work applies the results of Part I to error bounds for differentiable convex inclu- sions. A number of standard constraint qualifications for such inclusions are also examined. Keywords Weak sharp minima · Convex inclusion · Affine convex inclusion · Constraint qualification · Error bounds · Calmness Mathematics Subject Classification (2000) 90C25 · 90C31 · 49J52 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. J. V. Burke (B ) Department of Mathematics, University of Washington, Box # 354350, Seattle, WA 98195–4350, USA e-mail: burke@math.washington.edu S. Deng Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA e-mail: deng@math.niu.edu 123