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Weak sharp minima revisited. II: Application to linear regularity and error bounds. (English) Zbl 1124.90349
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.

90C31Sensitivity, stability, parametric optimization
49J52Nonsmooth analysis (other weak concepts of optimality)
Full Text: DOI
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