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Zbl 1124.90349
Burke, James V.; Deng, Sien
Weak sharp minima revisited. II: Application to linear regularity and error bounds. (English)
[J] Math. Program. 104, No. 2-3 (B), 235-261 (2005). ISSN 0025-5610; ISSN 1436-4646/e

Summary: 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 [Control Cybern. 31, No. 3, 439--469 (2002; Zbl 1105.90356)] 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.

MSC 2000:: *90C31 Sensitivity, etc.
49J52 Nonsmooth analysis (other weak concepts of optimality)

Keywords: weak sharp minima; local weak sharp minima; boundedly weak sharp minima; recession function; recession cone; linear regularity; additive regularity; constraint qualification; error bounds

Citations: Zbl 1105.90356

Cited in: Zbl 1163.90016

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